Relevant bibliographies by topics / Commutator estimates

Academic literature on the topic 'Commutator estimates'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Commutator estimates"

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Taylor, Michael. "Commutator estimates." Proceedings of the American Mathematical Society 131, no. 5 (September 19, 2002): 1501–7. http://dx.doi.org/10.1090/s0002-9939-02-06723-0.

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Chen, Dongxiang, Dan Zou, and Suzhen Mao. "Multiple Weighted Estimates for Vector-Valued Multilinear Singular Integrals with Non-Smooth Kernels and Its Commutators." Journal of Function Spaces and Applications 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/363916.

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This note concerns multiple weighted inequalities for vector-valued multilinear singular integral operator with nonsmooth kernel and its corresponding commutators containing multilinear commutator and iterated commutator generated by the vector-valued multilinear operator and BMO functions. By the weighted estimates for a class of new variant maximal and sharp maximal functions, the multiple weighted norm inequalities for such operators are obtained.
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Ber, A. F., and F. A. Sukochev. "Commutator estimates in $W^{*}$-factors." Transactions of the American Mathematical Society 364, no. 10 (October 1, 2012): 5571–87. http://dx.doi.org/10.1090/s0002-9947-2012-05568-1.

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Auscher, Pascal, and Michael E. Taylor. "Paradifferential operators and commutator estimates." Communications in Partial Differential Equations 20, no. 9-10 (January 1995): 1743–75. http://dx.doi.org/10.1080/03605309508821150.

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Ber, A. F., and F. A. Sukochev. "Commutator estimates in W⁎-algebras." Journal of Functional Analysis 262, no. 2 (January 2012): 537–68. http://dx.doi.org/10.1016/j.jfa.2011.09.018.

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Gao, Wen Hua. "Weighted BMO Estimates for Commutators of Riesz Transforms Associated with Schrödinger Operator." Applied Mechanics and Materials 303-306 (February 2013): 1613–17. http://dx.doi.org/10.4028/www.scientific.net/amm.303-306.1613.

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Schrödinger operator; Weighted BMO spaces; Reverse Hölder inequality; Commutator Abstract. In this paper, the Schrödinger operator on n dimensions Euclid space with the non-zero, nonnegative potential function satisfying the reverse Hölder inequality is considered. The weighted boundedness of the commutators composed of several Riesz transforms associated with the Schrödinger operator and weighted BMO function on weighted Lebesgue integral spaces are obtained, for some weighted function.
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Lai, Xudong. "Multilinear Estimates for Calderón Commutators." International Mathematics Research Notices 2020, no. 20 (August 31, 2018): 7097–138. http://dx.doi.org/10.1093/imrn/rny197.

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Abstract In this paper, we investigate the multilinear boundedness properties of the higher ($n$-th) order Calderón commutator for dimensions larger than two. We establish all multilinear endpoint estimates for the target space $L^{\frac{d}{d+n},\infty }(\mathbb{R}^d)$, including that Calderón commutator maps the product of Lorentz spaces $L^{d,1}(\mathbb{R}^d)\times \cdots \times L^{d,1}(\mathbb{R}^d)\times L^1(\mathbb{R}^d)$ to $L^{\frac{d}{d+n},\infty }(\mathbb{R}^d)$, which is the higher dimensional nontrivial generalization of the endpoint estimate that the $n$-th order Calderón commutator maps $L^{1}(\mathbb{R})\times \cdots \times L^{1}(\mathbb{R})\times L^1(\mathbb{R})$ to $L^{\frac{1}{1+n},\infty }(\mathbb{R})$. When considering the target space $L^{r}(\mathbb{R}^d)$ with $r<\frac{d}{d+n}$, some counterexamples are given to show that these multilinear estimates may not hold. The method in the present paper seems to have a wide range of applications and it can be applied to establish the similar results for Calderón commutator with a rough homogeneous kernel.
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Lenzmann, Enno, and Armin Schikorra. "Sharp commutator estimates via harmonic extensions." Nonlinear Analysis 193 (April 2020): 111375. http://dx.doi.org/10.1016/j.na.2018.10.017.

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Chen, Jiecheng, and Guoen Hu. "Weighted estimates for the Calderón commutator." Proceedings of the Edinburgh Mathematical Society 63, no. 1 (September 23, 2019): 169–92. http://dx.doi.org/10.1017/s001309151900021x.

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AbstractIn this paper the authors consider the weighted estimates for the Calderón commutator defined by \mathcal{C}_{m+1, A}(a_1,\ldots,a_{m};f)(x)={\rm p. v.} \displaystyle\int_{\mathbb{R}}\displaystyle\frac{P_2(A; x, y)\prod\nolimits_{j=1}^m(A_j(x)-A_j(y))}{(x-y)^{m+2}}f(y){\rm d}y,with P2(A;x, y) = A(x) − A(y) − A′(y)(x − y) and A′ ∈ BMO(ℝ). Dominating this operator by multi(sub)linear sparse operators, the authors establish the weighted bounds from $L^{p_1}(\mathbb {R},w_1) \times \cdots \times L^{p_{m+1}}(\mathbb {R},w_{m+1})$ to $L^{p}(\mathbb {R},\nu _{\vec {\kern 1pt w}})$, with p1, …, pm+1 ∈ (1, ∞), 1/p = 1/p1 + · · · + 1/pm+1, and $\vec {\kern 1pt w}=(w_1, \ldots , w_{m+1})\in A_{\vec {P}}(\mathbb {R}^{m+1})$. The authors also obtain the weighted weak type endpoint estimates for $\mathcal {C}_{m+1, A}$.
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Ber, A. F., and F. A. Sukochev. "Commutator estimates in von Neumann algebras." Functional Analysis and Its Applications 47, no. 1 (March 2013): 62–63. http://dx.doi.org/10.1007/s10688-013-0007-y.

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Dissertations / Theses on the topic "Commutator estimates"

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Potapov, Denis, and denis potapov@flinders edu au. "Lipschitz and commutator estimates, a unified approach." Flinders University. School of Informatics and Engineeering, 2007. http://catalogue.flinders.edu.au./local/adt/public/adt-SFU20070723.110059.

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The subject of the thesis is the study of operator functions in the setting of symmetric operator spaces. In this latter setting, it is of great importance to analyze the properties of so-called operator functions A --> f(A), where the variable A is a self-adjoint operator and f is a complex-valued Borel function on the real line. The thesis study the question of differentiability of this type of operator functions. The latter question is intimately related to the study of commutators. Text not only extends existing results to the setting of unbounded self-adjoint linear operators, but it is also shown that this can be obtained via a unified approach utilizing the left regular representation of von Neumann algebras.
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Hieber, Matthias, and Elmar Schrohe. "Lρ spectral independence of elliptic operators via commutator estimates." Universität Potsdam, 1997. http://opus.kobv.de/ubp/volltexte/2008/2504/.

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Let {Tsub(p) : q1 ≤ p ≤ q2} be a family of consistent Csub(0) semigroups on Lφ(Ω) with q1, q2 ∈ [1, ∞)and Ω ⊆ IRn open. We show that certain commutator conditions on Tφ and on the resolvent of its generator Aφ ensure the φ independence of the spectrum of Aφ for φ ∈ [q1, q2]. Applications include the case of Petrovskij correct systems with Hölder continuous coeffcients, Schrödinger operators, and certain elliptic operators in divergence form with real, but not necessarily symmetric, or complex coeffcients.
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Mandich, Marc Adrien. "Commutators, spectral analysis, and applications to discrete Schrödinger operators." Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0725/document.

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L’objet de cette thèse est l’étude spectrale et dynamique de systèmes de la mécanique quantique en utilisant des techniques de commutateurs. Deux parmi les trois articles présentés traitent l’opérateur de Schrödinger discret sur un réseau. Dans le premier article, un principe d’absorption limite est établi pour le Laplacien discret multidimensionnel perturbé par la somme d’un potentiel de type Wigner-von Neumann et d’un potentiel de type longue portée. Ce résultat implique notamment l’absolue continuité du spectre de cet Hamiltonien à certaines énergies. Dans le second article, nous considérons à nouveau l’opérateur de Schrödinger discret multidimensionnel dont le potentiel est de type longue portée. Il est démontré que les fonctions propres correspondant à des valeurs propres de l’Hamiltonien décroissent sous-exponentiellement lorsque ces dernières ne sont pas un seuil. En dimension un, il est démontré de surcroît que ces fonctions propres décroissent exponentiellement. Une conséquence de ceci est l’absence de valeurs propres dans la partie centrale du spectre délimité aux extrémités par des seuils. Le troisième article étudie des propriétés dynamiques d’Hamiltoniens vérifiant des hypothèses minimales dans la théorie des commutateurs. En se basant sur une estimation des vitesses minimales d’une part et une version améliorée du théorème du RAGE d’autre part, nous dérivons deux estimations de propagation pour cette famille d’Hamiltoniens. Ces estimations indiquent que les états du système se comportent dynamiquement de façon très similaire aux états de diffusion. Toutefois, ceci n’écarte pas la possibilité de spectre singulier continu
This thesis deals with the analysis of spectral and dynamical properties of quantum mechanical systems using techniques of operator commutators. Two of the three research papers that are presented deal exclusively with the discrete Schrödinger operators on the lattice. The first article proves a limiting absorption principle for the multi-dimensional discrete Laplacian perturbed by the sum of a Wigner-von Neumann potential and long-range potential. This result notably implies the absolute continuity of the spectrum of this Hamiltonian at certain energies. The second article proves that eigenfunctions corresponding to non-threshold eigenvalues of multidimensional discrete Schrödinger operators decay sub-exponentially. In one dimension, it is further proven that these eigenfunctions decay exponentially. A consequence of this is the absence of eigenvalues when the middle portion of the spectrum does not contain any thresholds. The third article investigates dynamical properties of Hamiltonians under very minimal assumptions in the theory of commutators. Based on minimal escape velocities and an improved version of the RAGE Theorem, we derive propagation estimates for these types of Hamiltonians. These estimates indicate that the states of the system behave dynamically very much like scattering states. Nonetheless, the existence of singularly continuous states cannot be disproved
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Pampana, Srilaxmi. "FPGA BASED IMPLEMENTATION OF A POSITION ESTIMATOR FOR CONTROLLING A SWITCHED RELUCTANCE MOTOR." UKnowledge, 2004. http://uknowledge.uky.edu/gradschool_theses/254.

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Rotor Position information is essential in the operation of the Switched Reluctance Motor (SRM) for properly controlling its phase currents. This thesis uses Field Programmable Gate Array (FPGA) technology to implement a method to estimate the SRMs rotor position using the inverse inductance value of the SRMs phases. The estimated rotor position is given as input to the Commutator circuit, also implemented in the FPGA, to determine when torque-producing currents should be input in the SRM phase windings. The Estimator and Commutator design is coded using Verilog HDL and is simulated using Xilinx tools. This circuit is implemented on a Xilinx Virtex XCV800 FPGA system. The experimentally generated output is validated by comparing it with simulation results from a Simulink model of the Estimator. The performance of the FPGA based SRM rotor position estimator in terms of calculation time is compared to a digital signal processor (DSP) implementation of the same position estimator algorithm. It is found that the FPGA rotor position Estimator with a 5MHz clock can update its rotor position estimate every 7s compared to an update time of 50s for a TMS320C6701-150 DSP implementation using a commercial DSP board. This is a greater than 7 to one reduction in the update time.
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Potapov, Denis Sergeevich. "Lipschitz and commutator estimates, a unified approach." 2007. http://catalogue.flinders.edu.au/local/adt/public/adt-SFU20070723.110059/index.html.

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Thesis (Ph.D.)--Flinders University, School of Informatics and Engineering, Dept. of Mathematics.
Typescript bound. Includes bibliographical references: (leaves 135-140) and index. Also available online.
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Israelsson, Anders. "Mathematical Foundations of Quantum Mechanics." Thesis, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-210078.

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Books on the topic "Commutator estimates"

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Isett, Philip. The Coarse Scale Flow and Commutator Estimates. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0016.

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This chapter derives estimates for the coarse scale flow and commutator. Instead of mollifying the velocity field in the time variable, it derives a Transport equation for vsubscript Element and some estimates that will be necessary for the proof. Here the quadratic term arises from the failure of the nonlinearity to commute with the averaging. Commutator estimates are then derived. To observe cancellation in the quadratic term, the control over the higher-frequency part of v is used, and cancellation is obtained from the lower-frequency parts. It becomes clear that the commutator terms can be estimated using the control of only the derivatives of v. The chapter concludes by presenting the theorem for coarse scale flow estimates.
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Isett, Philip. Stress Terms Not Involving Solving the Divergence Equation. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0025.

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This chapter estimates the terms in the new stress that do not involve solving the divergence equation. These terms are the Mollification terms and the Stress term. Throughout the estimates, Bsubscript Greek Small Letter Lamda will be assumed to be some constant. After considering the Mollification term from the velocity, the chapter introduces a proposition stating that for k = 0, … , L, there exist constants Cₖ depending on Bsubscript Greek Small Letter Lamda. It then estimates the material derivative, highlighting wastefulness in the estimate, and discusses a commutator estimate suggesting that it may be important to work with frequency energy levels of order L greater than or equal to 2. Finally, it presents the Mollification term from the stress as well as estimates for the Stress term.
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Book chapters on the topic "Commutator estimates"

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Lannes, David. "Product and commutator estimates." In Mathematical Surveys and Monographs, 283–95. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/surv/188/11.

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Le Floch, Yohann. "Proof of Product and Commutator Estimates." In CRM Short Courses, 97–113. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94682-5_8.

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Lu, Zhiqin, and David Wenzel. "Commutator Estimates Comprising the Frobenius Norm – Looking Back and Forth." In Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics, 533–59. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49182-0_22.

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Gesztesy, Fritz, Gilles Godefroy, Loukas Grafakos, and Igor Verbitsky. "A Unified Theory of Commutator Estimates for a Class of Interpolation Methods." In Nigel J. Kalton Selecta, 579–664. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-18799-0_16.

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Oswald, Peter, and Tatiana Shingel. "Commutator Estimate for Nonlinear Subdivision." In Mathematical Methods for Curves and Surfaces, 383–402. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-54382-1_22.

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Milman, Mario. "Estimates for commutators in real interpolation." In Lecture Notes in Mathematics, 95–126. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0073505.

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Matsuoka, Katsuo. "B σ-Campanato Estimates for Commutators of Calderón–Zygmund Operators." In Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation, 357–70. Basel: Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0648-0_22.

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Fang, Shizan, and Huaiqian Lee. "On the Estimate for Commutators in DiPerna–Lions Theory." In Stochastic Analysis with Financial Applications, 61–71. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0097-6_5.

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"Top-order pointwise commutator estimates involving the Eikonal function." In Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations, 283–93. Providence, Rhode Island: American Mathematical Society, 2016. http://dx.doi.org/10.1090/surv/214/15.

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"Decompositions and estimates for the commutators." In Series in Applied and Computational Mathematics, 35–46. WORLD SCIENTIFIC, 2014. http://dx.doi.org/10.1142/9789814641630_0003.

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Conference papers on the topic "Commutator estimates"

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Snell, Antony. "A Unified Method for Modeling 3 Phase Synchronous Machines." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-12483.

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The use of 3 phase synchronous machines (motor or generator) is becoming more widespread with the introduction of variable frequency drives, which allow the machines to be used very effectively as low maintenance alternatives to brushed DC commutator motors. However, mathematical modeling of these machines is often difficult to understand. Many textbooks on electro-mechanical machines introduce the synchronous machine using a phasor model of the voltages induced in the armature and the applied voltage. This yields some neat results of output torque as a function of the torque angle but fails to provide much insight into how this torque comes about. Furthermore, the method assumes that the resistance of the armature windings is negligible compared with armature reactance. The method falls apart when resistance must be included. Even when armature resistance is small, there is no insight into how efficiency is compromised by copper losses in the armature. The approach described in this paper is based on the same theory, which is usually used to explain the operation of DC commutator machines. This approach provides direct insight into how torque is developed. Losses introduced by armature resistance are included so reasonable efficiency estimates can be made. Meanwhile the neat results of the simple phasor model can be obtained as a special cases by setting armature resistance to zero.
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Zhi Huang and Kai Zhao. "Weighted endpoint estimate for the commutator of Marcinkiewicz integral." In 2010 Second International Conference on Communication Systems, Networks and Applications (ICCSNA). IEEE, 2010. http://dx.doi.org/10.1109/iccsna.2010.5588837.

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