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Author : Michael Eugene Taylor
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 50,8 Mb
Release : 1984
Category : Differential equations, Hypoelliptic
ISBN : 9780821823149
Author : Michael E. Taylor
Publisher : Unknown
Page : 182 pages
File Size : 51,7 Mb
Release : 1984
Category : Differential equations, Hypoelliptic
ISBN : OCLC:1103641041
Author : Luigi Rodino
Publisher : Springer Science & Business Media
Page : 449 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401156264
The NATO Advanced Study Institute "Microlocal Analysis and Spectral The ory" was held in Tuscany (Italy) at Castelvecchio Pascoli, in the district of Lucca, hosted by the international vacation center "11 Ciocco" , from September 23 to October 3, 1996. The Institute recorded the considerable progress realized recently in the field of Microlocal Analysis. In a broad sense, Microlocal Analysis is the modern version of the classical Fourier technique in solving partial differential equa tions, where now the localization proceeding takes place with respect to the dual variables too. Precisely, through the tools of pseudo-differential operators, wave-front sets and Fourier integral operators, the general theory of the lin ear partial differential equations is now reaching a mature form, in the frame of Schwartz distributions or other generalized functions. At the same time, Microlocal Analysis has grown up into a definite and independent part of Math ematical Analysis, with other applications all around Mathematics and Physics, one major theme being Spectral Theory for Schrodinger equation in Quantum Mechanics.
Author : Michael Eugene Taylor
Publisher : American Mathematical Soc.
Page : 328 pages
File Size : 44,5 Mb
Release : 1986
Category : Mathematics
ISBN : 9780821815236
This book explores some basic roles of Lie groups in linear analysis, with particular emphasis on the generalizations of the Fourier transform and the study of partial differential equations. It began as lecture notes for a one-semester graduate course given by the author in noncommutative harmonic analysis. It is a valuable resource for both graduate students and faculty, and requires only a background with Fourier analysis and basic functional analysis, plus the first few chapters of a standard text on Lie groups. The basic method of noncommutative harmonic analysis, a generalization of Fourier analysis, is to synthesize operators on a space on which a Lie group has a unitary representation from operators on irreducible representation spaces.Though the general study is far from complete, this book covers a great deal of the progress that has been made on important classes of Lie groups. Unlike many other books on harmonic analysis, this book focuses on the relationship between harmonic analysis and partial differential equations. The author considers many classical PDEs, particularly boundary value problems for domains with simple shapes, that exhibit noncommutative groups of symmetries. Also, the book contains detailed work, which has not previously been published, on the harmonic analysis of the Heisenberg group and harmonic analysis on cones.
Author : Daniel Grieser,Stefan Teufel,Andras Vasy
Publisher : Springer Science & Business Media
Page : 148 pages
File Size : 44,7 Mb
Release : 2012-12-13
Category : Mathematics
ISBN : 9783034804660
Microlocal analysis is a field of mathematics that was invented in the mid-20th century for the detailed investigation of problems from partial differential equations, which incorporated and made rigorous many ideas that originated in physics. Since then it has grown to a powerful machine which is used in global analysis, spectral theory, mathematical physics and other fields, and its further development is a lively area of current mathematical research. In this book extended abstracts of the conference 'Microlocal Methods in Mathematical Physics and Global Analysis', which was held at the University of Tübingen from the 14th to the 18th of June 2011, are collected.
Author : M. Salah Baouendi
Publisher : Unknown
Page : 264 pages
File Size : 51,7 Mb
Release : 1984
Category : Mathematics
ISBN : UCAL:B4405757
This volume is the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Microlocal Analysis and its Applications to Partial Differential Equations, held July 10-16, 1983 in Boulder, Colorado. It contains refereed articles which were delivered at the conference. Two of the papers are survey articles, one on uniqueness and non-uniqueness in the Cauchy problem and one on hypoanalytic structures; the rest are either detailed announcements or complete papers covering such areas as spectrum of operators, nonlinear problems, asymptotics, pseudodifferential operators of multiple characteristics and operators on groups and homogeneous spaces. The volume should be useful to active mathematicians and graduate students working on linear and nonlinear partial differential equations and related areas.
Author : Gerald B. Folland
Publisher : Princeton University Press
Page : 288 pages
File Size : 44,6 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882427
This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The principal features of the book are as follows: a thorough treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation; an exposition of the Weyl calculus of pseudodifferential operators, with emphasis on ideas coming from harmonic analysis and physics; a discussion of wave packet transforms and their applications; and a new development of Howe's theory of the oscillator semigroup.
Author : Alberto Parmeggiani
Publisher : Springer
Page : 260 pages
File Size : 48,6 Mb
Release : 2010-07-23
Category : Mathematics
ISBN : 9783642119224
This book grew out of a series of lectures given at the Mathematics Department of Kyushu University in the Fall 2006, within the support of the 21st Century COE Program (2003–2007) “Development of Dynamical Mathematics with High Fu- tionality” (Program Leader: prof. Mitsuhiro Nakao). It was initially published as the Kyushu University COE Lecture Note n- ber 8 (COE Lecture Note, 8. Kyushu University, The 21st Century COE Program “DMHF”, Fukuoka, 2008. vi+234 pp.), and in the present form is an extended v- sion of it (in particular, I have added a section dedicated to the Maslov index). The book is intended as a rapid (though not so straightforward) pseudodiff- ential introduction to the spectral theory of certain systems, mainly of the form a +a where the entries of a are homogeneous polynomials of degree 2 in the 2 0 2 n n (x,?)-variables, (x,?)? R×R,and a is a constant matrix, the so-called non- 0 commutative harmonic oscillators, with particular emphasis on a class of systems introduced by M. Wakayama and myself about ten years ago. The class of n- commutative harmonic oscillators is very rich, and many problems are still open, and worth of being pursued.
Author : Min-Teh Cheng,Xing-Wei Zhou,Dong-Gao Deng
Publisher : Springer
Page : 240 pages
File Size : 52,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540464747
All papers in this volume are original (fully refereed) research reports by participants of the special program on Harmonic Analysis held in the Nankai Institute of Mathematics. The main themes include: Wavelets, Singular Integral Operators, Extemal Functions, H Spaces, Harmonic Analysis on Local Domains and Lie Groups, and so on. See also :G. David "Wavelets and Singular Integrals on Curves and Surfaces", LNM 1465,1991. FROM THE CONTENTS: D.C. Chang: Nankai Lecture in -Neumann Problem.- T.P. Chen, D.Z. Zhang: Oscillary Integral with Polynomial Phase.- D.G. Deng, Y.S. Han: On a Generalized Paraproduct Defined by Non-Convolution.- Y.S. Han: H Boundedness of Calderon-Zygmund Operators for Product Domains.- Z.X. Liu, S.Z. Lu: Applications of H|rmander Multiplier Theorem to Approximation in Real Hardy Spaces.- R.L. Long, F.S. Nie: Weighted Sobolev Inequality and Eigenvalue Estimates of Schr|dinger Operator.- A. McIntosh, Q. Tao: Convolution Singular Integral Operators on Lipschitz Curves.- Z.Y. Wen, L.M.Wu, Y.P. Zhang: Set of Zeros of Harmonic Functions of Two Variables.- C.K. Yuan: On the Structures of Locally Compact Groups Admitting Inner Invariant Means.
Author : Michael Ruzhansky,Ville Turunen
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 50,8 Mb
Release : 2014-01-18
Category : Mathematics
ISBN : 9783319025506
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.”
Author : Alan L. Carey
Publisher : American Mathematical Soc.
Page : 361 pages
File Size : 45,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821851999
This volume contains articles related to the conference ``Motives, Quantum Field Theory, and Pseudodifferntial Operators'' held at Boston University in June 2008, with partial support from the Clay Mathematics Institute, Boston University, and the National Science Foundation. There are deep but only partially understood connections between the three conference fields, so this book is intended both to explain the known connections and to offer directions for further research. In keeping with the organization of the conference, this book contains introductory lectures on each of the conference themes and research articles on current topics in these fields. The introductory lectures are suitable for graduate students and new Ph.D.'s in both mathematics and theoretical physics, as well as for senior researchers, since few mathematicians are expert in any two of the conference areas. Among the topics discussed in the introductory lectures are the appearance of multiple zeta values both as periods of motives and in Feynman integral calculations in perturbative QFT, the use of Hopf algebra techniques for renormalization in QFT, and regularized traces of pseudodifferential operators. The motivic interpretation of multiple zeta values points to a fundamental link between motives and QFT, and there are strong parallels between regularized traces and Feynman integral techniques. The research articles cover a range of topics in areas related to the conference themes, including geometric, Hopf algebraic, analytic, motivic and computational aspects of quantum field theory and mirror symmetry. There is no unifying theory of the conference areas at present, so the research articles present the current state of the art pointing towards such a unification.
Author : Luigi Rodino,Bert-Wolfgang Schulze,Man Wah Wong
Publisher : American Mathematical Soc.
Page : 432 pages
File Size : 52,5 Mb
Release : 2007-11-21
Category : Mathematics
ISBN : 0821871552
This volume is based on lectures given at the workshop on pseudo-differential operators held at the Fields Institute from December 11, 2006 to December 15, 2006. The two main themes of the workshop and hence this volume are partial differential equations and time-frequency analysis. The contents of this volume consist of five mini-courses for graduate students and post-docs, and fifteen papers on related topics. Of particular interest in this volume are the mathematical underpinnings, applications and ramifications of the relatively new Stockwell transform, which is a hybrid of the Gabor transform and the wavelet transform. The twenty papers in this volume reflect modern trends in the development of pseudo-differential operators.
Author : William O. Bray,P. Milojevic,C.V. Stanojevic
Publisher : CRC Press
Page : 465 pages
File Size : 47,6 Mb
Release : 2020-12-17
Category : Mathematics
ISBN : 9781000117134
Providing complete expository and research papers on the geometric and analytic aspects of Fourier analysis, this work discusses new approaches to classical problems in the theory of trigonometric series, singular integrals/pseudo-differential operators, Fourier analysis on various groups, numerical aspects of Fourier analysis and their applications, wavelets and more.
Author : Salvador Pérez-Esteva,Carlos Villegas-Blas
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 49,6 Mb
Release : 2000
Category : Geometric quantization
ISBN : 9780821821152
The first Summer School of Analysis and Mathematical Physics of the Universidad Nacional Autónoma de México (Cuernavaca) offered graduate and advanced undergraduate students courses on modern topics in the overlap between analysis and physics. This volume contains the expanded notes from the lectures by Brian Hall, Alejandro Uribe, and David Borthwick. The articles introduce readers to mathematical methods of classical and quantum mechanics and the link between these two theories: quantization and semiclassical analysis. Hall writes about holomorphic methods in analysis and mathematical physics and includes exercises. Uribe's lectures covered trace formulae, in particular asymptotic behavior and the relationship between the asymptotics and the geometric properties of the classical system. Borthwick presents an introduction to Kähler quantization, including the moment map, the orbit method, and symmetry and reduction. The exposition in the entire volume is geared to introducing graduate students with a basic knowledge of mathematics into areas of active research. This volume is a joint publication of the American Mathematical Society and the Sociedad Matematica Mexicana. Members of the SMM may order directly from the AMS at the AMS member price.
Author : Vladimir Georgiev,Tohru Ozawa,Michael Ruzhansky,Jens Wirth
Publisher : Springer Nature
Page : 317 pages
File Size : 47,8 Mb
Release : 2020-11-07
Category : Mathematics
ISBN : 9783030582159
This book originates from the session "Harmonic Analysis and Partial Differential Equations" held at the 12th ISAAC Congress in Aveiro, and provides a quick overview over recent advances in partial differential equations with a particular focus on the interplay between tools from harmonic analysis, functional inequalities and variational characterisations of solutions to particular non-linear PDEs. It can serve as a useful source of information to mathematicians, scientists and engineers. The volume contains contributions of authors from a variety of countries on a wide range of active research areas covering different aspects of partial differential equations interacting with harmonic analysis and provides a state-of-the-art overview over ongoing research in the field. It shows original research in full detail allowing researchers as well as students to grasp new aspects and broaden their understanding of the area.