Relevant bibliographies by topics / Spherical maximal functions

Academic literature on the topic 'Spherical maximal functions'

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Published: 6 September 2023

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Journal articles on the topic "Spherical maximal functions"

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Lacey, Michael T. "Sparse bounds for spherical maximal functions." Journal d'Analyse Mathématique 139, no. 2 (October 2019): 613–35. http://dx.doi.org/10.1007/s11854-019-0070-2.

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Seeger, Andreas, Stephen Wainger, and James Wright. "Spherical Maximal Operators on Radial Functions." Mathematische Nachrichten 187, no. 1 (1997): 241–65. http://dx.doi.org/10.1002/mana.19971870112.

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Duoandikoetxea, Javier, Adela Moyua, and Osane Oruetxebarria. "The spherical maximal operator on radial functions." Journal of Mathematical Analysis and Applications 387, no. 2 (March 2012): 655–66. http://dx.doi.org/10.1016/j.jmaa.2011.09.028.

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Kajima, Yasuhiro. "Spherical functions on orthogonal groups." Nagoya Mathematical Journal 141 (March 1996): 157–82. http://dx.doi.org/10.1017/s0027763000005572.

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Let G be a p-adic connected reductive algebraic group and K a maximal compact subgroup of G. In [4], Casselman obtained the explicit formula of zonal spherical functions on G with respect to K on the assumption that K is special. It is known (Bruhat and Tits [3]) that the affine root system of algebraic group which has good but not special maximal compact subgroup is A1 C2, or Bn (n > 3), and all Bn-types can be realized by orthogonal groups. Here the assumption “good” is necessary for the Satake’s theory of spherical functions.
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Kesler, Robert, Michael T. Lacey, and Darío Mena. "Sparse bounds for the discrete spherical maximal functions." Pure and Applied Analysis 2, no. 1 (January 1, 2020): 75–92. http://dx.doi.org/10.2140/paa.2020.2.75.

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Gauthier, P. M., and J. Xiao. "Functions of bounded expansion: normal and Bloch functions." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 66, no. 2 (April 1999): 168–88. http://dx.doi.org/10.1017/s144678870003929x.

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AbstractNormal functions and Bloch functions are respectively functions of bounded spherical expansion and bounded Euclidean expansion. In this paper we discuss the behaviour of normal functions and of Bloch functions in terms of the maximal ideal space of H∞, the Bergman projection and the Ahlfors-Shimizu characteristic.
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Roos, Joris, and Andreas Seeger. "Spherical maximal functions and fractal dimensions of dilation sets." American Journal of Mathematics 145, no. 4 (August 2023): 1077–110. http://dx.doi.org/10.1353/ajm.2023.a902955.

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abstract: For the spherical mean operators $\scr{A}_t$ in $\Bbb{R}^d$, $d\ge 2$, we consider the maximal functions $M_Ef=\sup_{t\in E}|\scr{A}_t f|$, with dilation sets $E\subset [1,2]$. In this paper we give a surprising characterization of the closed convex sets which can occur as closure of the sharp $L^p$ improving region of $M_E$ for some $E$. This region depends on the Minkowski dimension of $E$, but also other properties of the fractal geometry such as the Assouad spectrum of $E$ and subsets of $E$. A key ingredient is an essentially sharp result on $M_E$ for a class of sets called (quasi-)Assouad regular which is new in two dimensions.
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Anderson, Theresa C., and Eyvindur Ari Palsson. "Bounds for discrete multilinear spherical maximal functions in higher dimensions." Bulletin of the London Mathematical Society 53, no. 3 (January 22, 2021): 855–60. http://dx.doi.org/10.1112/blms.12465.

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Dosidis, Georgios, and Loukas Grafakos. "On families between the Hardy–Littlewood and spherical maximal functions." Arkiv för Matematik 59, no. 2 (2021): 323–43. http://dx.doi.org/10.4310/arkiv.2021.v59.n2.a4.

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Leckband, Mark. "A note on the spherical maximal operator for radial functions." Proceedings of the American Mathematical Society 100, no. 4 (April 1, 1987): 635. http://dx.doi.org/10.1090/s0002-9939-1987-0894429-9.

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Dissertations / Theses on the topic "Spherical maximal functions"

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Hait, Sourav. "Sparse bounds for various spherical maximal functions." Thesis, 2020. https://etd.iisc.ac.in/handle/2005/4551.

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Harmonic analysis mainly deals with the qualitative and quantitative properties of functions and transforms of those functions. It has applications in various areas of Mathematics like PDE, Differential geometry, Ergodic theory etc and also in several areas of Physics like Classical and Quantum mechanics etc and this makes it a very attractive area of study. The theory of spherical means plays a very crucial role in the field of Classical harmonic analysis. In 1976, E.M.Stein first studied the boundedness properties of maximal function associated to spherical means taken over the Euclidean sphere. Theory of spherical means taken over geodesic spheres in different Lie groups and Symmetric spaces has received considerable attention in the last few decades. In this thesis, we consider various versions of spherical maximal function, mainly on Euclidean space and its non-commutative neighbour Heisenberg group
NBHM
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Book chapters on the topic "Spherical maximal functions"

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Myronenko, Andriy, Xubo Song, and David J. Sahn. "Maximum Likelihood Motion Estimation in 3D Echocardiography through Non-rigid Registration in Spherical Coordinates." In Functional Imaging and Modeling of the Heart, 427–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-01932-6_46.

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Lee, Sanghyuk, Keith M. Rogers, and Andreas Seeger. "Square Functions and Maximal Operators Associated with Radial Fourier Multipliers." In Advances in Analysis, edited by Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, Stephen Wainger, Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, and Stephen Wainger. Princeton University Press, 2014. http://dx.doi.org/10.23943/princeton/9780691159416.003.0012.

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This chapter begins with an overview on square functions for spherical and Bochner–Riesz means which were introduced by Eli Stein, and discusses their implications for radial multipliers and associated maximal functions. It focuses on the Littlewood–Paley bounds for two square functions introduced by Stein, who had stressed their importance in harmonic analysis and many important variants and generalizations in various monographs. The chapter proves new endpoint estimates for these square functions, for the maximal Bochner–Riesz operator, and for more general classes of radial Fourier multipliers. The majority of the chapter is devoted to these proofs, such as for convolutions with spherical measures.
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Córdoba, A. "Restriction Lemmas, Spherical Summation, Maximal Functions, Square Functions and All That." In North-Holland Mathematics Studies, 57–64. Elsevier, 1985. http://dx.doi.org/10.1016/s0304-0208(08)70280-9.

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"The spherical maximal function." In Graduate Studies in Mathematics, 301–18. Providence, Rhode Island: American Mathematical Society, 2023. http://dx.doi.org/10.1090/gsm/224/11.

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"The lacunary spherical maximal function." In Graduate Studies in Mathematics, 319–37. Providence, Rhode Island: American Mathematical Society, 2023. http://dx.doi.org/10.1090/gsm/224/12.

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Piretzidis, Dimitrios, Christopher Kotsakis, Stelios P. Mertikas, and Michael G. Sideris. "Spatio-Spectral Assessment of Some Isotropic Polynomial Covariance Functions on the Sphere." In International Association of Geodesy Symposia. Berlin, Heidelberg: Springer Berlin Heidelberg, 2023. http://dx.doi.org/10.1007/1345_2023_190.

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AbstractIn gravity field modeling, covariance functions are mainly associated with least squares collocation. Prior to the implementation of least squares collocation, the characteristics of the selected analytical covariance function need to be well understood. In this contribution, we study four polynomial covariance functions, i.e., the spherical, Askey, C2-Wendland and C4-Wendland models. All of them are defined on the sphere and correspond to isotropic, positive definite and compactly supported functions. We examine them in the spatial and spectral domains, and assess their characteristics, such as the correlation length, the curvature parameter, the spectral maximum and the spectral decay rate. We also provide analytical expressions and numerical estimates for these parameters.
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K. Uzunoglu, Nikolaos. "Bio-Simulation of the Induction of Forced Resonance Mechanical Oscillations to Virus Particles by Non-Ionizing Electromagnetic Radiation: Prospects as an Anti-Virus Modality." In Biomimetics - Bridging the Gap [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.106802.

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The induction of acoustic-mechanical oscillations to virus particles by illuminating them with microwave signals is analyzed theoretically. Assuming the virus particle is of spherical shape, its capsid consisting primarily of glycoproteins, a viscous fluid model is adopted while the outside medium of the sphere is taken to be the ideal fluid. The electrical charge distribution of virus particles is assumed to be spherically symmetric with a variation along the radius. The generated acoustic-mechanical oscillations are computed by solving a boundary value problem analytically, making use of Green’s function approach. Resonance conditions to achieve maximum energy transfer from microwave radiation to acoustic oscillation to the particle are investigated. Estimation of the feasibility of the technique to compete with virus epidemics either for sterilization of spaces or for future therapeutic applications is examined briefly.
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"Problems of Harmonic Analysis Related to Finite-Type Hypersurfaces in R3, and Newton Polyhedra Detlef Müller." In Advances in Analysis, edited by Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, Stephen Wainger, Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, and Stephen Wainger. Princeton University Press, 2014. http://dx.doi.org/10.23943/princeton/9780691159416.003.0013.

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This chapter presents three sets of problems and explains how these questions can be answered in an (almost) complete way in terms of Newton polyhedra associated to the given surface S (here, a smooth, finite type hypersurface in R³ with Riemannian surface measure dσ‎). The first problem is a classical question about estimates for oscillatory integrals, and there exists a huge body of results on it, in particular for convex hypersurfaces. The other two problems had first been formulated by Stein: the study of maximal averages along hypersurfaces has been initiated in Stein's work on the spherical maximal function, and also the idea of Fourier restriction goes back to him.
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Aschenbrenner, Matthias, Lou van den Dries, and Joris van der Hoeven. "Eventual Quantities, Immediate Extensions, and Special Cuts." In Asymptotic Differential Algebra and Model Theory of Transseries. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691175423.003.0012.

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This chapter deals with eventual quantities, immediate extensions, and special cuts. It first considers the behavior of eventual quantities before discussing Newton weight, Newton degree, and Newton multiplicity as well as Newton weight of linear differential operators. It then establishes the following result: Every asymptotically maximal H-asymptotic field with rational asymptotic integration is spherically complete. The chapter proceeds by describing special (definable) cuts in H-asymptotic fields K with asymptotic integration and introducing some key elementary properties of K, namely λ‎-freeness and ω‎-freeness, which indicate that these cuts are not realized in K. It shows that has these properties. Finally, it looks at certain special existentially definable subsets of Liouville closed H-fields K, along with the behavior of the functions ω‎ and λ‎ on these sets.
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Conference papers on the topic "Spherical maximal functions"

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Alexander, Dennis R., John P. Barton, Scott A. Schaub, and Mark E. Emanuel. "Scattered internal and external near fields for spherical and cylinderlike particles." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1987. http://dx.doi.org/10.1364/oam.1987.we1.

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Calculations of the electric-field strengths internal and external to the particle but in the near field have been performed for both spheres and infinite cylinders. Results are presented that illustrate the magnitude of the internal and external electric-field strengths in terms of a source function defined as S = |E/Einc|2. The location of the maximum source function external to the particle depends on the optical size parameter. For example, a spherical aerosol particle of water with an optical size of 12–13 and an index of refraction of 1.18 + 0.07 i has a maximum source function of ~3.25 occurring at a normalized radial position of ~1.8 radii on the shadow side.
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Bahrami, M., M. M. Yovanovich, and J. R. Culham. "A Compact Model for Spherical Rough Contacts." In ASME/STLE 2004 International Joint Tribology Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/trib2004-64015.

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The contact of rough spheres is of high interest in many tribological, thermal, and electrical fundamental analyses. Implementing the existing models is complex and requires iterative numerical solutions. In this paper a new model is presented and a general pressure distribution is proposed that encompasses the entire range of spherical rough contacts including the Hertzian limit. It is shown that the non-dimensional maximum contact pressure is the key parameter that controls the solution. Compact expressions are proposed for calculating the pressure distribution, radius of the contact area, elastic bulk deformation, and the compliance as functions of the governing non-dimensional parameters. The present model shows the same trends as those of the Greenwood and Tripp model. Correlations proposed for the contact radius and the compliance are compared with experimental data collected by others and good agreement is observed.
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Kai, Li, and A. D'Alessio. "Electromagnetic field resonance at the interface of two concentric spheres." In The European Conference on Lasers and Electro-Optics. Washington, D.C.: Optica Publishing Group, 1994. http://dx.doi.org/10.1364/cleo_europe.1994.cthi46.

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For homogeneous spheres irradiated by infinite, electromagnetic plane waves (Fig. 1), existence of extremely strong sharp maxima in the extinction efficiency curves as a function of size parameter was found analytically by the so-called Mie theory for a long time.1 Excellent coincidences of the maxima of the calculated extinction efficiency as a function of wavelength for a homogeneous sphere with the spikes on the spectra of a laser power to levitate a homogeneous spherical particle at a fixed height when varying the wavelength of the laser beam have been found.2,3 Since the volume averaged electric density inside a sphere at a resonant state is several orders higher than that inside a sphere at a nonresonant state,4 even a laser beam of small intensity may cause nonelastic emissions. In fact, spikes on spectra of fluorescence emission and stimulated Raman scattering coincide excellently with the maxima of the calculated extinction efficiency spectra by using the Mie theory.3 According to Chylek,4 the basic period (Δx) of the double-peak structure on the Q ext - x curve is a monotonous function of refractive index m, given that x≫1, where the size parameter is defined by x = 2πα/λ, λ is the wavelength. Thereby, the MDRs have been used to measure sizes and refractive indices of spherical particles and optical fibres with an accuracy several orders higher than any other optical methods. The MDRs is seen to be a powerful tool in the field of particle characterisation.
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Nayebi, A. "Effect of Nonlinear Kinematic Hardening Constants on Cyclic Spherical Indentation Test." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-24005.

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In the last decade, instrumented indentation test has been widely used to determine the mechanical properties of different materials and especially for metals. The mechanical properties such as Young modulus, yield stress, hardening exponent, and stress-strain curve were determined with the help of the load–displacement curve of the continuous indentation test. The method consists of pushing an indenter in a material sample and the applied load and the indenter displacement are measured. In this research the load on the indenter was considered as cyclic and varied from zero to Fmax. Because of the Bauschinger effect, the hysteresis loops were formed. With the help of these hysteresis loops, nonlinear kinematic hardening parameters of the Armstrong–Freiderick (A-F) model can be determined. Spherical indenter was used and the sample was considered isotropic. The material behavior was modeled by the A-F rule. The test was modeled by the finite element method. An axi-symmetric mesh was used. The A–F model constants, C and γ, were varied to obtain their effects on the hysteresis loops. Maximum applied load was considered constant for different finite element modeling and the maximum and residual displacements were calculated from the simulations results. The normalized maximum and the residual displacements were increased as a function of the cycles. It was shown that these parameters value and their rate are dependent on the material model constants. These dependences were shown for different examples which can help to characterize the A-F model constants by the cyclic spherical indentation tests.
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Curtis, Colin W., and Michael L. Calvisi. "Axisymmetric Model of an Intracranial Saccular Aneurysm: Theory and Computation." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-66383.

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An axisymmetric model of an intracranial saccular aneurysm is presented and analyzed. The model assumes a simplified spherical geometry for the aneurysm in order to develop insight into the mechanisms that effect wall shear stress and deformation of the membrane. A theoretical model is first developed based on Stokes’ equations for viscous flow in order to derive a stream function that describes vortical flow inside a sphere representative of flow inside a real aneurysm. This flow pattern is implemented in a finite element model of a spherical aneurysm using the software COMSOL Multiphysics. The results indicate close agreement between the theoretical and computational models in terms of the flow streamlines and location of the maximum wall shear stress. Furthermore, the computational model accounts for the deformation and stress of the membrane, showing regions of maximum tension and compression at opposite poles of the saccular membrane. This work elucidates many important results regarding the mechanics of saccular aneurysms and provides a basis for developing more physiologically realistic analyses.
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Saidimanesh, Mahdi, Azin Shahiri, and Ali Nikparto. "Simulation and Optimization of a Semi Spherical Air Bearing." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-87334.

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It is important to test the attitude control systems on satellites before they are launched in space. Traditionally this has been done by dropping the satellite, and firing the thrusters before the satellite makes a soft landing in a net. This method only allows a few seconds of testing and does not lend itself to the measurement of pointing accuracy. A better method is to mount the satellite on a spherical air bearing. In this paper behavior of a semi spherical air bearing is studied and analyzed in various conditions. These bearings are used in different applications such as simulation of approximately frictionless condition which is the satellite’s situation in space. In this analysis FLUENT 6.3.26 is used to simulate the air bearing’s behavior. Simulation process is divided into 5 sections. These sections are accordingly 2dimensional with static boundary condition, 3dimensional and static, 2dimensional and dynamic and 3dimensional and dynamic boundary conditions. At last bearing’s function was optimized by changing some adjustable parameters which are important in controlling the bearings behavior such as air entering nozzles diameter and their number and location. Importance of this study is to simulate the behavior of the bearing in dynamic boundary condition using dynamic mesh. Eventually results of the simulation are compared to the actual test results and bearing behavior is analyzed. Finally best arrangement for achieving maximum normal load is studied.
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Mohaghegh, Fazlolah, and H. S. Udaykumar. "A Simplified Model for the Normal Collision of Arbitrary Shape Particles in a Viscous Flow." In ASME 2017 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/fedsm2017-69366.

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Modeling collision of finite size arbitrarily shaped particles is a tedious task because of difficulties in finding the collision parameter for the non-spherical particles. These parameters include the contact point, direction of the collision force and the collision forces and moments. In this paper a new collision algorithm is proposed to simulate collision of arbitrary shape particles to tackle flows containing a large number of particles. A pseudo-potential function is defined to quantify the collision parameters. This potential is defined based on the distance from the particle interface using either level set method or an analytical representation. With this definition, we can find the direction of collision forces and the amount of overlapping during the collision course. The collision forces are applied through a spring with a coefficient defined based on the collision course. In order to apply the damping, after the maximum collision course is achieved a spring with a lower stiffness in devised to achieve the desired bounce velocity. The results are validated for a spherical particle colliding with a wall. Then we show the capability of the model in simulation of collision of non-spherical particles with a wall. The new collision method not only is simple to implement but also it is applicable for any particle shape.
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Bean, Charles P. "Reflections from Large Rippled Surfaces of Water." In Light and Color in the Open Air. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/lcoa.1990.thb5.

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Under the title of this paper, Minnaert1 discusses the work of Hulburt2 on the reflection of the sun by ocean waves. If the sun is low enough, one sees a bright patch of reflected light that is more or less triangular in shape with the base at the horizon. The position of the tip of the patch depends on the height of the observer above the water while its angular width at the horizon is quite invariant. Hulburt calculated this width at the horizon on the assumption that the waves were randomly oriented reflecting surfaces of a given maximum slope. He numerically calculated this width as a function of the maximum slope of the wave and the altitude of the sun. Hulburt stated2 that this relationship "is easily written down from spherical trigonometry but is too long to give here; it is made of six equations with parameters which may not readily be eliminated."
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Takahira, Hiroyuki, and Yoshinori Jinbo. "Application of an Improved Ghost Fluid Method to the Collapse of Non-Spherical Bubbles in a Compressible Liquid." In ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajk2011-04027.

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The ghost fluid method (GFM) is improved to investigate violent bubble collapse in a compressible liquid, in which the adaptive mesh refinement with multigrids, the surface tension, and the thermal diffusion through the bubble interface are taken into account. The improved multigrid GFM is applied to the interaction of an incident shock wave with a bubble. The multigrid GFM captures the fine interfacial and vortex structures of the toroidal bubble when the bubble collapses violently accompanied with the penetration of the liquid jet and the formation of the shock waves. The multigrid GFM is also applied to the bubble collapse near a tissue surface in which the tissue is modeled with gelatin in order to predict the tissue damage due to the bubble collapse; the motions of three phases for the gas inside the bubble, the liquid surrounding the bubble, and the gelatin boundary are solved directly by coupling the level set method with the improved GFM. Two kinds of level set functions are utilized for distinguishing the gas-liquid interface from the liquid-gelatin interface. It is shown that the impact of the shock waves generated from the collapsing bubble on the boundary leads to the formation of depression of the boundary; the toroidal bubble penetrates into the depression. Also, the surface tension effects are successfully included in the improved GFM. The thermal effects of internal gas on the bubble collapse are also discussed by considering the thermal diffusion across the interface in the GFM. The thermal boundary layers of the toroidal bubble are captured with the method. The result shows that the smaller the initial bubble radius becomes, the lower the maximum temperature inside the bubble becomes because of the thermal diffusion across the interface.
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Kulkarni, Sudhir, Saurabh Tonapi, Pierre Larochelle, and Kunal Mitra. "Effect of Tracking Flat Reflector Using Novel Auxiliary Drive Mechanism on the Performance of Stationary Photovoltaic Module." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-42973.

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General ways of cost reduction in solar power generation are Solar Tracked Photovoltaic (PV) arrays and concentrator systems. The PV array tracking becomes infeasible with increase in the size of the array and concentrated system is ineffective for continuous power generation as it requires external cooling system. Proposed approach here is to employ a novel auxiliary mirror drive mechanism to track the sun and reflect the rays on to stationary PV arrays. The performance is compared with same PV module without reflector under the same environmental conditions. Solarex SX 38 PV module and cleardome solar reflector (96% reflectivity) are used for the experiments. PV module is connected to electrical load through Maximum Power Point Tracker (MPPT) and data acquisition system for voltage and current measurements. Incident radiation is measured using Li-Cor pyranometers located on the plane of the module and horizontal plane. A shadow band device is used for the measurement of diffuse solar radiation. The PV module is placed facing south at a tilt angle equal to the latitude angle. A reflector is placed facing north and oriented using the novel Mirror Positioning Device (MPD). The MPD is a five bar spherical mechanism used for solar tracking. This mechanism has two degrees of freedom which allows for tracking the sun along its azimuth and altitude. The mechanism is driven by two servo motors which actuate two links. The actuated link 1 helps in achieving the altitude gained by the sun while the actuated link 2 helps to attain the azimuth (or horizontal movement). The reason for using a spherical mechanism is due to the virtue of its architecture; it allows for carrying a larger payload and also helps in reducing weight. Its advantages are that it requires less power than traditional PV array tracking; there is no need for sensors to determine the position of the sun and also that it being a two degree of freedom spherical mechanism yields a large singularity free mirror orienting workspace. Solar radiation, efficiency, and temperature are plotted as a function of time for analysis. Average diffuse solar radiation is found to be in the range of 15 to 20% of total solar radiation. Different experiments are performed to find out the optimum cycle speed for reflector. Measurements show that output from the PV panel can be increased in the order of 22% with the use of tracking reflector. This work has succeeded in its goal in realization that the considerable increase in output power from PV modules can be achieved.
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