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Global Pseudo Differential Calculus On Euclidean Spaces
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Book Synopsis Global Pseudo-differential Calculus on Euclidean Spaces by : Fabio Nicola
Download or read book Global Pseudo-differential Calculus on Euclidean Spaces written by Fabio Nicola and published by Springer Science & Business Media. This book was released on 2011-01-30 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a global pseudo-differential calculus in Euclidean spaces, which includes SG as well as Shubin classes and their natural generalizations containing Schroedinger operators with non-polynomial potentials. This calculus is applied to study global hypoellipticity for several pseudo-differential operators. The book includes classic calculus as a special case. It will be accessible to graduate students and of benefit to researchers in PDEs and mathematical physics.
Book Synopsis Pseudo-Differential Operators and Symmetries by : Michael V. Ruzhansky
Download or read book Pseudo-Differential Operators and Symmetries written by Michael V. Ruzhansky and published by Springer Science & Business Media. This book was released on 2009-10-19 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the development of the theory of pseudo-di?erential n operators on spaces with symmetries. Such spaces are the Euclidean space R ,the n torus T , compact Lie groups and compact homogeneous spaces. The book consists of several parts. One of our aims has been not only to present new results on pseudo-di?erential operators but also to show parallels between di?erent approaches to pseudo-di?erential operators on di?erent spaces. Moreover, we tried to present the material in a self-contained way to make it accessible for readers approaching the material for the ?rst time. However, di?erent spaces on which we develop the theory of pseudo-di?er- tial operators require di?erent backgrounds. Thus, while operators on the - clidean space in Chapter 2 rely on the well-known Euclidean Fourier analysis, pseudo-di?erentialoperatorsonthetorusandmoregeneralLiegroupsinChapters 4 and 10 require certain backgrounds in discrete analysis and in the representation theory of compact Lie groups, which we therefore present in Chapter 3 and in Part III,respectively. Moreover,anyonewhowishestoworkwithpseudo-di?erential- erators on Lie groups will certainly bene?t from a good grasp of certain aspects of representation theory. That is why we present the main elements of this theory in Part III, thus eliminating the necessity for the reader to consult other sources for most of the time. Similarly, the backgrounds for the theory of pseudo-di?erential 3 operators on S and SU(2) developed in Chapter 12 can be found in Chapter 11 presented in a self-contained way suitable for immediate use.
Book Synopsis Operator Theory, Pseudo-Differential Equations, and Mathematical Physics by : Yuri I. Karlovich
Download or read book Operator Theory, Pseudo-Differential Equations, and Mathematical Physics written by Yuri I. Karlovich and published by Springer Science & Business Media. This book was released on 2012-10-30 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of papers devoted to the 70th birthday of Professor Vladimir Rabinovich. The opening article (by Stefan Samko) includes a short biography of Vladimir Rabinovich, along with some personal recollections and bibliography of his work. It is followed by twenty research and survey papers in various branches of analysis (pseudodifferential operators and partial differential equations, Toeplitz, Hankel, and convolution type operators, variable Lebesgue spaces, etc.) close to Professor Rabinovich's research interests. Many of them are written by participants of the International workshop “Analysis, Operator Theory, and Mathematical Physics” (Ixtapa, Mexico, January 23–27, 2012) having a long history of scientific collaboration with Vladimir Rabinovich, and are partially based on the talks presented there.The volume will be of great interest to researchers and graduate students in differential equations, operator theory, functional and harmonic analysis, and mathematical physics.
Book Synopsis Pseudo-Differential Operators and Generalized Functions by : Stevan Pilipović
Download or read book Pseudo-Differential Operators and Generalized Functions written by Stevan Pilipović and published by Birkhäuser. This book was released on 2015-04-27 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers peer-reviewed contributions representing modern trends in the theory of generalized functions and pseudo-differential operators. It is dedicated to Professor Michael Oberguggenberger (Innsbruck University, Austria) in honour of his 60th birthday. The topics covered were suggested by the ISAAC Group in Generalized Functions (GF) and the ISAAC Group in Pseudo-Differential Operators (IGPDO), which met at the 9th ISAAC congress in Krakow, Poland in August 2013. Topics include Columbeau algebras, ultra-distributions, partial differential equations, micro-local analysis, harmonic analysis, global analysis, geometry, quantization, mathematical physics, and time-frequency analysis. Featuring both essays and research articles, the book will be of great interest to graduate students and researchers working in analysis, PDE and mathematical physics, while also offering a valuable complement to the volumes on this topic previously published in the OT series.
Book Synopsis Time-Frequency Analysis of Operators by : Elena Cordero
Download or read book Time-Frequency Analysis of Operators written by Elena Cordero and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-09-21 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative text studies pseudodifferential and Fourier integral operators in the framework of time-frequency analysis, providing an elementary approach, along with applications to almost diagonalization of such operators and to the sparsity of their Gabor representations. Moreover, Gabor frames and modulation spaces are employed to study dispersive equations such as the Schrödinger, wave, and heat equations and related Strichartz problems. The first part of the book is addressed to non-experts, presenting the basics of time-frequency analysis: short time Fourier transform, Wigner distribution and other representations, function spaces and frames theory, and it can be read independently as a short text-book on this topic from graduate and under-graduate students, or scholars in other disciplines.
Book Synopsis Mathematical Analysis and Applications—Plenary Lectures by : Luigi G. Rodino
Download or read book Mathematical Analysis and Applications—Plenary Lectures written by Luigi G. Rodino and published by Springer. This book was released on 2018-11-11 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes the texts of the survey lectures given by plenary speakers at the 11th International ISAAC Congress held in Växjö, Sweden, on 14-18 August, 2017. It is the purpose of ISAAC to promote analysis, its applications, and its interaction with computation. Analysis is understood here in the broad sense of the word, including differential equations, integral equations, functional analysis, and function theory. With this objective, ISAAC organizes international Congresses for the presentation and discussion of research on analysis. The plenary lectures in the present volume, authored by eminent specialists, are devoted to some exciting recent developments, topics including: local solvability for subprincipal type operators; fractional-order Laplacians; degenerate complex vector fields in the plane; lower bounds for pseudo-differential operators; a survey on Morrey spaces; localization operators in Signal Theory and Quantum Mechanics. Thanks to the accessible style used, readers only need a basic command of Calculus. This book will appeal to scientists, teachers, and graduate students in Mathematics, in particular Mathematical Analysis, Probability and Statistics, Numerical Analysis and Mathematical Physics.
Book Synopsis Quantization, PDEs, and Geometry by : Dorothea Bahns
Download or read book Quantization, PDEs, and Geometry written by Dorothea Bahns and published by Birkhäuser. This book was released on 2016-02-11 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics. Specifically, it discusses global aspects of elliptic PDEs, Berezin-Toeplitz quantization, the stability of solitary waves, and sub-Riemannian geometry. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen. The authors explain fundamental concepts and ideas and present them clearly. Starting from basic notions, these course notes take the reader to the point of current research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. All contributions are of interest to researchers in the respective fields, but they are also accessible to graduate students.
Book Synopsis Fourier Analysis by : Michael Ruzhansky
Download or read book Fourier Analysis written by Michael Ruzhansky and published by Springer Science & Business Media. This book was released on 2014-01-18 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis. It is based on lectures given at the international conference “Fourier Analysis and Pseudo-Differential Operators,” June 25–30, 2012, at Aalto University, Finland. This collection of 20 refereed articles is based on selected talks and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series “Fourier Analysis and Partial Differential Equations.”
Book Synopsis Advances in Microlocal and Time-Frequency Analysis by : Paolo Boggiatto
Download or read book Advances in Microlocal and Time-Frequency Analysis written by Paolo Boggiatto and published by Springer Nature. This book was released on 2020-03-03 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume gathers contributions to the conference Microlocal and Time-Frequency Analysis 2018 (MLTFA18), which was held at Torino University from the 2nd to the 6th of July 2018. The event was organized in honor of Professor Luigi Rodino on the occasion of his 70th birthday. The conference’s focus and the contents of the papers reflect Luigi’s various research interests in the course of his long and extremely prolific career at Torino University.
Book Synopsis Wave Packet Analysis of Feynman Path Integrals by : Fabio Nicola
Download or read book Wave Packet Analysis of Feynman Path Integrals written by Fabio Nicola and published by Springer Nature. This book was released on 2022-07-28 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this monograph is to offer an accessible and essentially self-contained presentation of some mathematical aspects of the Feynman path integral in non-relativistic quantum mechanics. In spite of the primary role in the advancement of modern theoretical physics and the wide range of applications, path integrals are still a source of challenging problem for mathematicians. From this viewpoint, path integrals can be roughly described in terms of approximation formulas for an operator (usually the propagator of a Schrödinger-type evolution equation) involving a suitably designed sequence of operators. In keeping with the spirit of harmonic analysis, the guiding theme of the book is to illustrate how the powerful techniques of time-frequency analysis - based on the decomposition of functions and operators in terms of the so-called Gabor wave packets – can be successfully applied to mathematical path integrals, leading to remarkable results and paving the way to a fruitful interaction. This monograph intends to build a bridge between the communities of people working in time-frequency analysis and mathematical/theoretical physics, and to provide an exposition of the present novel approach along with its basic toolkit. Having in mind a researcher or a Ph.D. student as reader, we collected in Part I the necessary background, in the most suitable form for our purposes, following a smooth pedagogical pattern. Then Part II covers the analysis of path integrals, reflecting the topics addressed in the research activity of the authors in the last years.
Book Synopsis Operator Theory, Operator Algebras, and Matrix Theory by : Carlos André
Download or read book Operator Theory, Operator Algebras, and Matrix Theory written by Carlos André and published by Birkhäuser. This book was released on 2018-08-22 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of invited survey articles and research papers in the scientific areas of the “International Workshop on Operator Algebras, Operator Theory and Applications,” which was held in Lisbon in July 2016. Reflecting recent developments in the field of algebras of operators, operator theory and matrix theory, it particularly focuses on groupoid algebras and Fredholm conditions, algebras of approximation sequences, C* algebras of convolution type operators, index theorems, spectrum and numerical range of operators, extreme supercharacters of infinite groups, quantum dynamics and operator algebras, and inverse eigenvalue problems. Establishing bridges between the three related areas of operator algebras, operator theory, and matrix theory, the book is aimed at researchers and graduate students who use results from these areas.
Book Synopsis Born-Jordan Quantization by : Maurice A. de Gosson
Download or read book Born-Jordan Quantization written by Maurice A. de Gosson and published by Springer. This book was released on 2016-01-11 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive mathematical study of the operators behind the Born–Jordan quantization scheme. The Schrödinger and Heisenberg pictures of quantum mechanics are equivalent only if the Born–Jordan scheme is used. Thus, Born–Jordan quantization provides the only physically consistent quantization scheme, as opposed to the Weyl quantization commonly used by physicists. In this book we develop Born–Jordan quantization from an operator-theoretical point of view, and analyze in depth the conceptual differences between the two schemes. We discuss various physically motivated approaches, in particular the Feynman-integral point of view. One important and intriguing feature of Born-Jordan quantization is that it is not one-to-one: there are infinitely many classical observables whose quantization is zero.
Book Synopsis Landscapes of Time-Frequency Analysis by : Paolo Boggiatto
Download or read book Landscapes of Time-Frequency Analysis written by Paolo Boggiatto and published by Springer. This book was released on 2019-01-30 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters in this volume are based on talks given at the inaugural Aspects of Time-Frequency Analysis conference held in Turin, Italy from July 5-7, 2017, which brought together experts in harmonic analysis and its applications. New connections between different but related areas were presented in the context of time-frequency analysis, encouraging future research and collaborations. Some of the topics covered include: Abstract harmonic analysis, Numerical harmonic analysis, Sampling theory, Compressed sensing, Mathematical signal processing, Pseudodifferential operators, and Applications of harmonic analysis to quantum mechanics. Landscapes of Time-Frequency Analysis will be of particular interest to researchers and advanced students working in time-frequency analysis and other related areas of harmonic analysis.
Book Synopsis Analysis and Partial Differential Equations: Perspectives from Developing Countries by : Julio Delgado
Download or read book Analysis and Partial Differential Equations: Perspectives from Developing Countries written by Julio Delgado and published by Springer. This book was released on 2019-01-27 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents current trends in analysis and partial differential equations from researchers in developing countries. The fruit of the project 'Analysis in Developing Countries', whose aim was to bring together researchers from around the world, the volume also includes some contributions from researchers from developed countries. Focusing on topics in analysis related to partial differential equations, this volume contains selected contributions from the activities of the project at Imperial College London, namely the conference on Analysis and Partial Differential Equations held in September 2016 and the subsequent Official Development Assistance Week held in November 2016. Topics represented include Fourier analysis, pseudo-differential operators, integral equations, as well as related topics from numerical analysis and bifurcation theory, and the countries represented range from Burkina Faso and Ghana to Armenia, Kyrgyzstan and Tajikistan, including contributions from Brazil, Colombia and Cuba, as well as India and China. Suitable for postgraduate students and beyond, this volume offers the reader a broader, global perspective of contemporary research in analysis.
Book Synopsis Integral Fourier Operators by : Michèle Audin
Download or read book Integral Fourier Operators written by Michèle Audin and published by Universitätsverlag Potsdam. This book was released on 2018-04-17 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of contributions based on lectures delivered at a school on Fourier Integral Operators held in Ouagadougou, Burkina Faso, 14–26 September 2015, provides an introduction to Fourier Integral Operators (FIO) for a readership of Master and PhD students as well as any interested layperson. Considering the wide spectrum of their applications and the richness of the mathematical tools they involve, FIOs lie the cross-road of many a field. This volume offers the necessary background, whether analytic or geometric, to get acquainted with FIOs, complemented by more advanced material presenting various aspects of active research in that area.
Book Synopsis Symplectic Methods in Harmonic Analysis and in Mathematical Physics by : Maurice A. de Gosson
Download or read book Symplectic Methods in Harmonic Analysis and in Mathematical Physics written by Maurice A. de Gosson and published by Springer Science & Business Media. This book was released on 2011-07-30 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to give a rigorous and complete treatment of various topics from harmonic analysis with a strong emphasis on symplectic invariance properties, which are often ignored or underestimated in the time-frequency literature. The topics that are addressed include (but are not limited to) the theory of the Wigner transform, the uncertainty principle (from the point of view of symplectic topology), Weyl calculus and its symplectic covariance, Shubin’s global theory of pseudo-differential operators, and Feichtinger’s theory of modulation spaces. Several applications to time-frequency analysis and quantum mechanics are given, many of them concurrent with ongoing research. For instance, a non-standard pseudo-differential calculus on phase space where the main role is played by “Bopp operators” (also called “Landau operators” in the literature) is introduced and studied. This calculus is closely related to both the Landau problem and to the deformation quantization theory of Flato and Sternheimer, of which it gives a simple pseudo-differential formulation where Feichtinger’s modulation spaces are key actors. This book is primarily directed towards students or researchers in harmonic analysis (in the broad sense) and towards mathematical physicists working in quantum mechanics. It can also be read with profit by researchers in time-frequency analysis, providing a valuable complement to the existing literature on the topic. A certain familiarity with Fourier analysis (in the broad sense) and introductory functional analysis (e.g. the elementary theory of distributions) is assumed. Otherwise, the book is largely self-contained and includes an extensive list of references.
Book Synopsis Pseudo-Differential Operators and Symmetries by : Michael Ruzhansky
Download or read book Pseudo-Differential Operators and Symmetries written by Michael Ruzhansky and published by Springer Science & Business Media. This book was released on 2009-12-29 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the development of the theory of pseudo-di?erential n operators on spaces with symmetries. Such spaces are the Euclidean space R ,the n torus T , compact Lie groups and compact homogeneous spaces. The book consists of several parts. One of our aims has been not only to present new results on pseudo-di?erential operators but also to show parallels between di?erent approaches to pseudo-di?erential operators on di?erent spaces. Moreover, we tried to present the material in a self-contained way to make it accessible for readers approaching the material for the ?rst time. However, di?erent spaces on which we develop the theory of pseudo-di?er- tial operators require di?erent backgrounds. Thus, while operators on the - clidean space in Chapter 2 rely on the well-known Euclidean Fourier analysis, pseudo-di?erentialoperatorsonthetorusandmoregeneralLiegroupsinChapters 4 and 10 require certain backgrounds in discrete analysis and in the representation theory of compact Lie groups, which we therefore present in Chapter 3 and in Part III,respectively. Moreover,anyonewhowishestoworkwithpseudo-di?erential- erators on Lie groups will certainly bene?t from a good grasp of certain aspects of representation theory. That is why we present the main elements of this theory in Part III, thus eliminating the necessity for the reader to consult other sources for most of the time. Similarly, the backgrounds for the theory of pseudo-di?erential 3 operators on S and SU(2) developed in Chapter 12 can be found in Chapter 11 presented in a self-contained way suitable for immediate use.
