Relevant bibliographies by topics / Quaternionic function theory

Academic literature on the topic 'Quaternionic function theory'

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Published: 10 March 2023

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Journal articles on the topic "Quaternionic function theory"

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Kim, Ji, and Kwang Shon. "Expansion of implicit mapping theory to split-quaternionic maps in Clifford analysis." Filomat 35, no. 11 (2021): 3833–40. http://dx.doi.org/10.2298/fil2111833k.

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This paper presents the regularity of a split-quaternionic function and a corresponding split- Cauchy-Riemann system of a split quaternion. The properties of an inverse and an implicit mapping theory for a split-quaternionic map are investigated. In addition, the paper proposes a definition and expression for a split biregular mapping in an open set in C2. The obtained results are illustrated with some examples.
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Pap, Margit, and Ferenc Schipp. "Quaternionic Blaschke Group." Mathematics 7, no. 1 (December 31, 2018): 33. http://dx.doi.org/10.3390/math7010033.

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In the complex case, the Blaschke group was introduced and studied. It turned out that in the complex case this group plays important role in the construction of analytic wavelets and multiresolution analysis in different analytic function spaces. The extension of the wavelet theory to quaternion variable function spaces would be very beneficial in the solution of many problems in physics. A first step in this direction is to give the quaternionic analogue of the Blaschke group. In this paper we introduce the quaternionic Blaschke group and we study the properties of this group and its subgroups.
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Gentili, Graziano, and Caterina Stoppato. "Geometric function theory over quaternionic slice domains." Journal of Mathematical Analysis and Applications 495, no. 2 (March 2021): 124780. http://dx.doi.org/10.1016/j.jmaa.2020.124780.

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Morais, J., and M. A. Pérez-de la Rosa. "Towards a quaternionic function theory linked with the Lamé's wave functions." Mathematical Methods in the Applied Sciences 38, no. 17 (January 19, 2015): 4365–87. http://dx.doi.org/10.1002/mma.3376.

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Alpay, Daniel, Fabrizio Colombo, and Irene Sabadini. "Perturbation of the generator of a quaternionic evolution operator." Analysis and Applications 13, no. 04 (April 28, 2015): 347–70. http://dx.doi.org/10.1142/s0219530514500249.

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The theory of slice hyperholomorphic functions, introduced in recent years, has important applications in operator theory. The quaternionic version of this function theory and its Cauchy formula yield to a definition of the quaternionic version of the Riesz–Dunford functional calculus which is based on the notion of S-spectrum. This quaternionic functional calculus allows to define the quaternionic evolution operator which appears in the quaternionic version of quantum mechanics proposed by J. von Neumann and later developed by S. L. Adler. Generation results such as the Hille–Phillips–Yosida theorem have been recently proved. In this paper, we study the perturbation of the generator. The motivation of this study is that, as it happens in the classical case of closed complex linear operators, to verify the generation conditions of the Hille–Phillips–Yosida theorem, in the concrete cases, is often difficult. Thus in this paper we study the generation problem from the perturbation point of view. Precisely, given a quaternionic closed operator T that generates the evolution operator [Formula: see text] we study under which condition a closed operator P is such that T + P generates the evolution operator [Formula: see text]. This paper is addressed to people working in different research areas such as hypercomplex analysis and operator theory.
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Konno, Norio, Kaname Matsue, Hideo Mitsuhashi, and Iwao Sato. "Quaternionic quantum walks of Szegedy type and zeta functions of graphs." Quantum Information and Computation 17, no. 15&16 (December 2017): 1349–71. http://dx.doi.org/10.26421/qic17.15-16-6.

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We define a quaternionic extension of the Szegedy walk on a graph and study its right spectral properties. The condition for the transition matrix of the quaternionic Szegedy walk on a graph to be quaternionic unitary is given. In order to derive the spectral mapping theorem for the quaternionic Szegedy walk, we derive a quaternionic extension of the determinant expression of the second weighted zeta function of a graph. Our main results determine explicitly all the right eigenvalues of the quaternionic Szegedy walk by using complex right eigenvalues of the corresponding doubly weighted matrix. We also show the way to obtain eigenvectors corresponding to right eigenvalues derived from those of doubly weighted matrix.
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Abreu Blaya, Ricardo, Juan Bory Reyes, Alí Guzmán Adán, and Uwe Kaehler. "On some structural sets and a quaternionic (φ,ψ)-hyperholomorphic function theory." Mathematische Nachrichten 288, no. 13 (April 14, 2015): 1451–75. http://dx.doi.org/10.1002/mana.201300072.

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Shpakivskyi, V. S., and T. S. Kuzmenko. "Integral theorems for the quaternionic G-monogenic mappings." Analele Universitatii "Ovidius" Constanta - Seria Matematica 24, no. 2 (June 1, 2016): 271–81. http://dx.doi.org/10.1515/auom-2016-0042.

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Abstract In the paper [1] considered a new class of quaternionic mappings, so- called G-monogenic mappings. In this paper we prove analogues of classical integral theorems of the holomorphic function theory: the Cauchy integral theorems for surface and curvilinear integrals, and the Cauchy integral formula for G-monogenic mappings.
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Shapiro, M. V., and N. L. Vasilevski. "Quaternionic ψ-hyperholomorphic functions, singular integral operators and boundary value problems I. ψ-hyperholomorphic function theory." Complex Variables, Theory and Application: An International Journal 27, no. 1 (January 1995): 17–46. http://dx.doi.org/10.1080/17476939508814803.

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Kravchenko, V. V., and M. V. Shapiro. "Helmholtz operator with a quaternionic wave number and associated function theory. II. Integral representations." Acta Applicandae Mathematicae 32, no. 3 (September 1993): 243–65. http://dx.doi.org/10.1007/bf01082451.

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Dissertations / Theses on the topic "Quaternionic function theory"

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STOPPATO, CATERINA. "Regular functions of one quaternionic variable." Doctoral thesis, 2010. http://hdl.handle.net/2158/1034111.

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SARFATTI, GIULIA. "Elements of function theory in the unit ball of quaternions." Doctoral thesis, 2013. http://hdl.handle.net/2158/806320.

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The theory of regular functions over the quaternions introduced by Gentili and Struppa in 2006, already quite rich, is in continuous development. Despite their diverse peculiarities, regular functions reproduce numerous properties of holomorphic functions of one complex variable. This Thesis is devoted to investigate properties of regular functions defined on the unit ball B of the quaternions H. As it happens in the complex case, this particular subset of H represents a special domain for the class of regular function. It is the simplest example of the most natural set of definition for a regular function, namely of a "symmetric slice domain". Furthermore, on open balls centred at the origin, regular functions are characterized by having a power series expansion, hence they behave very nicely. The first Chapter, starting from the very first definitions, includes all the preliminary results that will be used in the sequel. The second Chapter discusses some properties of the modulus of regular functions, in particular how it is related with the modulus of the "regular conjugate" of a regular function. The main result presented is an analogue of the Borel-Carathéodory Theorem, a tool useful to bound the modulus of a regular function by means of the modulus of its real part. The central part of the Thesis contains geometric theory results. The third Chapter contains the analogue of the Bohr Theorem concerning power series, together with a weaker version, that follows as in the complex case from the Borel-Carathéodory Theorem. In the fourth Chapter we prove a Bloch-Landau type theorem, showing that in some sense the image of a ball under a regular function can not be too much thin. The fifth Chapter is dedicated to Landau-Toeplitz type theorems, that study the possible shapes that the image of a regular function can assume. The last Chapter is devoted to the study of the quaternionic Hardy spaces. We begin by the definition of the spaces H^p(B) and H^{\infty}(B), then we prove some of their basic properties. We introduce in conclusion the Corona Problem in the quaternionic setting, proving a partial statement of the Corona Theorem.
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Ross, Jenny Lee 1976. "Gröbner basis theory and its applications for regular and biregular functions." Thesis, 2010. http://hdl.handle.net/2152/ETD-UT-2010-05-1504.

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This paper covers basic theory of Grobner Bases and an algebraic analysis of the linear constant coefficient partial differential operators, specifically the Cauchy-Fueter operator. We will review examples and theory of regular and biregular functions in several quaternionic variables.
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Hopkins, Kimberly Michele. "Periods of modular forms and central values of L-functions." Thesis, 2010. http://hdl.handle.net/2152/ETD-UT-2010-05-1423.

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This thesis is comprised of three problems in number theory. The introduction is Chapter 1. The first problem is to partially generalize the main theorem of Gross, Kohnen and Zagier to higher weight modular forms. In Chapter 2, we present two conjectures which do this and some partial results towards their proofs as well as numerical examples. This work provides a new method to compute coefficients of weight k+1/2 modular forms for k>1 and to compute the square roots of central values of L-functions of weight 2k>2 modular forms. Chapter 3 presents four different interpretations of the main construction in Chapter 2. In particular we prove our conjectures are consistent with those of Beilinson and Bloch. The second problem in this thesis is to find an arithmetic formula for the central value of a certain Hecke L-series in the spirit of Waldspurger's results. This is done in Chapter 4 by using a correspondence between special points in Siegel space and maximal orders in quaternion algebras. The third problem is to find a lower bound for the cardinality of the principal genus group of binary quadratic forms of a fixed discriminant. Chapter 5 is joint work with Jeffrey Stopple and gives two such bounds.
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Books on the topic "Quaternionic function theory"

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Sabadini, Irene, and Sorin G. Gal. Quaternionic Approximation: With Application to Slice Regular Functions. Springer International Publishing AG, 2019.

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(Editor), Daniel Alpay, and Victor Vinnikov (Editor), eds. System Theory, the Schur Algorithm and Multidimensional Analysis (Operator Theory: Advances and Applications). Birkhäuser Basel, 2007.

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Gantner, Jonathan. Operator Theory on One-Sided Quaternion Linear Spaces: Intrinsic $S$-Functional Calculus and Spectral Operators. American Mathematical Society, 2021.

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System Theory, the Schur Algorithm and Multidimensional Analysis. Springer London, Limited, 2007.

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Hardy, Duncan. Conclusion. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198827252.003.0014.

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It is clear from the comparative study of Upper German evidence undertaken in this book that multilateral associations were ubiquitous in the Holy Roman Empire in the period 1346–1521, and that they structured the interactions of all the diverse political actors within it. Indeed, inhabitants of the late medieval Empire used an ‘associative’ language of membership and mutual assistance, and the multilateral metaphor of the Quaternion (a symbolic amalgam of political actors of various statuses), when attempting to apprehend and articulate the structure and function of their polity. Modern unitary concepts of statehood and constitutionality, which dominate how we narrate and describe late medieval and early modern history, are inadequate to make sense of the Empire’s structure. The paradigm of ‘associative political culture’ offered in this book therefore not only reconceptualizes the Empire, but also has implications for alternative ways of envisioning political configurations and developments in pre-modern Europe.
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Book chapters on the topic "Quaternionic function theory"

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Eriksson, Sirkka-Liisa, and Heikki Orelma. "Quaternionic Hyperbolic Function Theory." In Trends in Mathematics, 25–52. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-23854-4_2.

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Gürlebeck, Klaus, and Wolfgang Sprößig. "Discrete Quaternionic Function Theory." In Quaternionic Analysis and Elliptic Boundary Value Problems, 153–209. Basel: Birkhäuser Basel, 1989. http://dx.doi.org/10.1007/978-3-0348-7295-9_6.

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Martin, Mircea. "Function Spaces in Quaternionic and Clifford Analysis." In Operator Theory, 1393–422. Basel: Springer Basel, 2015. http://dx.doi.org/10.1007/978-3-0348-0667-1_24.

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Martin, Mircea. "Function Spaces in Quaternionic and Clifford Analysis." In Operator Theory, 1–26. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0692-3_24-1.

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Kravchenko, V. V., and M. V. Shapiro. "Helmholtz Operator with a Quaternionic Wave Number and Associated Function Theory." In Deformations of Mathematical Structures II, 101–28. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1896-5_3.

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Królikowski, Wiesław, and R. Michael Porter. "Biregular Quaternionic Functions." In Clifford Algebras and their Applications in Mathematical Physics, 129–35. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2006-7_15.

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Colombo, Fabrizio, Jonathan Gantner, and David P. Kimsey. "Slice Hyperholomorphic Functions." In Spectral Theory on the S-Spectrum for Quaternionic Operators, 11–51. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-03074-2_2.

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Colombo, Fabrizio, Jonathan Gantner, and David P. Kimsey. "The H∞-Functional Calculus." In Spectral Theory on the S-Spectrum for Quaternionic Operators, 137–49. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-03074-2_6.

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Colombo, Fabrizio, Jonathan Gantner, and David P. Kimsey. "The S-Functional Calculus for Unbounded Operators." In Spectral Theory on the S-Spectrum for Quaternionic Operators, 125–36. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-03074-2_5.

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Colombo, Fabrizio, Jonathan Gantner, and David P. Kimsey. "The F-Functional Calculus for Bounded Operators." In Spectral Theory on the S-Spectrum for Quaternionic Operators, 151–76. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-03074-2_7.

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Conference papers on the topic "Quaternionic function theory"

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Luna-Elizarrarás, María Elena, Ramón M. Rodríguez-Dagnino, Michael Shapiro, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "On a Version of Quaternionic Function Theory Related to Mathieu Functions." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790264.

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Morais, J. "A version of quaternionic function theory related to prolate spheroidal wave signals." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825417.

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Khmelnytskaya, Kira V. "Green function for the Maxwell system in chiral media using quaternionic analysis." In 2008 International Conference on Mathematical Methods in Electromagnetic Theory (MEET). IEEE, 2008. http://dx.doi.org/10.1109/mmet.2008.4580960.

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Ramirez Tachiquin, M. P., V. D. Sanchez Nava, and A. Fleiz Jaso. "On the solutions of the electrical impedance equation, applying quaternionic analysis and pseudoanalytic function theory." In 2008 International Conference on Mathematical Methods in Electromagnetic Theory (MEET). IEEE, 2008. http://dx.doi.org/10.1109/mmet.2008.4580935.

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Tachiquin, M. P. Ramirez, O. Rodriguez Torres, and J. J. Gutierrez Cortes. "New exact solutions for the three-dimensional Electrical Impedance Equation applying quaternionic analysis and pseudoanalytic function theory." In 2009 6th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE 2009). IEEE, 2009. http://dx.doi.org/10.1109/iceee.2009.5393346.

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Grigoriev, Yu. "Radial integration method in quaternion function theory and its applications." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4912654.

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Moore, B., and E. Oztop. "Redundancy Parameterization for Flexible Motion Control." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28387.

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Our overall research interest is in synthesizing human like reaching and grasping using anthropomorphic robot hand-arm systems, as well as understanding the principles underlying human control of these actions. When one needs to define the control and task requirements in the Cartesian space, the problem of inverse kinematics needs to be solved. For non-redundant manipulators, a desired end-effector position and orientation can be achieved by a finite number of solutions. For redundant manipulators however, there are in general infinitely many solutions where the cardinality of the solution set must be made finite by imposing certain constraints. In this paper, we consider the Mitsubishi PA10 manipulator which is similar to the human arm, in the sense that both wrist and shoulder joints can be considered to emulate a 3DOF ball joint. We explicitly derive the analytic solution for the inverse kinematics using quaternions. Then, we derive a parameterization in terms of a pure quaternion called the swivel quaternion. The swivel quaternion is similar to the elbow swivel angle used in most approaches, but avoid the computation of inverse trigonometric functions. This parameterization of the self-motion manifold is continuous with any end-effector motion. Given the pose of the end-effector and the swivel quaternion (or swivel angle), the algorithm derives all solution of the inverse kinematics (finite number). We then show how the parameterization of the elbow self-motion can be used for the real-time control of the PA10 manipulator in the presence of obstacles.
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Grigor’ev, Yuri M. "Quaternionic functions and their applications in mechanics of continua." In 6TH INTERNATIONAL CONFERENCE ON PRODUCTION, ENERGY AND RELIABILITY 2018: World Engineering Science & Technology Congress (ESTCON). Author(s), 2018. http://dx.doi.org/10.1063/1.5079386.

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Hou, Wenzheng, Qianqian Xu, Ke Ma, Qianxiu Hao, and Qingming Huang. "Quaternion Ordinal Embedding." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/287.

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Ordinal embedding (OE) aims to project objects into a low-dimensional space while preserving their ordinal constraints as well as possible. Generally speaking, a reasonable OE algorithm should simultaneously capture a) semantic meaning and b) the ordinal relationship of the objects. However, most of the existing methods merely focus on b). To address this issue, our goal in this paper is to seek a generic OE method to embrace the two features simultaneously. We argue that different dimensions of vector-based embedding are naturally entangled with each other. To realize a), we expect to decompose the D dimensional embedding space into D different semantic subspaces, where each subspace is associated with a matrix representation. Unfortunately, introducing a matrix-based representation requires far more complex parametric space than its vector-based counterparts. Thanks to the algebraic property of quaternions, we are able to find a more efficient way to represent a matrix with quaternions. For b), inspired by the classic chordal Grassmannian distance, a new distance function is defined to measure the distance between different quaternions/matrices, on top of which we construct a generic OE loss function. Experimental results for different tasks on both simulated and real-world datasets verify the effectiveness of our proposed method.
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Ruth, D. Alan, and J. Michael McCarthy. "SphinxPC: An Implementation of Four Position Synthesis for Planar and Spherical 4R Linkages." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/dac-3860.

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Abstract This paper presents the basic theory and algorithmic structure of a design system that implements four position synthesis for both planar and spherical four bar linkages. The formalism uses complex numbers to define the equation of a planar triangle and quaternions to define the equation of a spherical triangle. These equations form the basis of a parallel implementation of these design theories. The theory and major functional components of SphinxPC are described and examples are presented.
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