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Author: Alain Grigis
Publisher: Cambridge University Press
Published: 1994-03-03
Total Pages: 164
ISBN-13: 9780521449861
DOWNLOAD EBOOKThis book corresponds to a graduate course given many times by the authors, and should prove to be useful to mathematicians and theoretical physicists.
Author: Lamberto Cattabriga
Publisher: Springer
Published: 2006-11-14
Total Pages: 357
ISBN-13: 3540466037
DOWNLOAD EBOOKCONTENTS: J.M. Bony: Analyse microlocale des equations aux derivees partielles non lineaires.- G.G. Grubb: Parabolic pseudo-differential boundary problems and applications.- L. H|rmander: Quadratic hyperbolic operators.- H. Komatsu: Microlocal analysis in Gevrey classes and in complex domains.- J. Sj|strand: Microlocal analysis for the periodic magnetic Schr|dinger equation and related questions.
Author: Goro Kato
Publisher: CRC Press
Published: 2020-08-11
Total Pages: 320
ISBN-13: 1000148394
DOWNLOAD EBOOK"Provides a thorough introduction to the algebraic theory of systems of differential equations, as developed by the Japanese school of M. Sato and his colleagues. Features a complete review of hyperfunction-microfunction theory and the theory of D-modules. Strikes the perfect balance between analytic and algebraic aspects."
Author: Maciej Zworski
Publisher: American Mathematical Soc.
Published: 2012
Total Pages: 448
ISBN-13: 0821883208
DOWNLOAD EBOOK"...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.
Author: Sigurdur Helgason
Publisher: Springer Science & Business Media
Published: 1999-08-01
Total Pages: 214
ISBN-13: 9780817641092
DOWNLOAD EBOOKThe Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications, namely to partial differential equations, group representations, X-ray technology, nuclear magnetic resonance scanning, and tomography. This second edition, significantly expanded and updated, presents new material taking into account some of the progress made in the field since 1980. Aimed at beginning graduate students, this monograph will be useful in the classroom or as a resource for self-study. Readers will find here an accessible introduction to Radon transform theory, an elegant topic in integral geometry.
Author: André Bach
Publisher: Springer Science & Business Media
Published: 2013-03-14
Total Pages: 193
ISBN-13: 1475744951
DOWNLOAD EBOOKThis book presents the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics in a pedagogical, way and is mainly addressed to non-specialists in the subject. It is based on lectures taught by the author over several years, and includes many exercises providing outlines of useful applications of the semi-classical theory.
Author: Masaki Kashiwara
Publisher: American Mathematical Soc.
Published: 2003
Total Pages: 276
ISBN-13: 9780821827666
DOWNLOAD EBOOKMasaki Kashiwara is undoubtedly one of the masters of the theory of $D$-modules, and he has created a good, accessible entry point to the subject. The theory of $D$-modules is a very powerful point of view, bringing ideas from algebra and algebraic geometry to the analysis of systems of differential equations. It is often used in conjunction with microlocal analysis, as some of the important theorems are best stated or proved using these techniques. The theory has been used very successfully in applications to representation theory. Here, there is an emphasis on $b$-functions. These show up in various contexts: number theory, analysis, representation theory, and the geometry and invariants of prehomogeneous vector spaces. Some of the most important results on $b$-functions were obtained by Kashiwara. A hot topic from the mid '70s to mid '80s, it has now moved a bit more into the mainstream. Graduate students and research mathematicians will find that working on the subject in the two-decade interval has given Kashiwara a very good perspective for presenting the topic to the general mathematical public.
Author: Frédéric Pham
Publisher: Springer Science & Business Media
Published: 2011-04-22
Total Pages: 218
ISBN-13: 0857296035
DOWNLOAD EBOOKBringing together two fundamental texts from Frédéric Pham’s research on singular integrals, the first part of this book focuses on topological and geometrical aspects while the second explains the analytic approach. Using notions developed by J. Leray in the calculus of residues in several variables and R. Thom’s isotopy theorems, Frédéric Pham’s foundational study of the singularities of integrals lies at the interface between analysis and algebraic geometry, culminating in the Picard-Lefschetz formulae. These mathematical structures, enriched by the work of Nilsson, are then approached using methods from the theory of differential equations and generalized from the point of view of hyperfunction theory and microlocal analysis. Providing a ‘must-have’ introduction to the singularities of integrals, a number of supplementary references also offer a convenient guide to the subjects covered. This book will appeal to both mathematicians and physicists with an interest in the area of singularities of integrals. Frédéric Pham, now retired, was Professor at the University of Nice. He has published several educational and research texts. His recent work concerns semi-classical analysis and resurgent functions.
Author: Michael Eugene Taylor
Publisher: American Mathematical Soc.
Published: 1984
Total Pages: 188
ISBN-13: 0821823140
DOWNLOAD EBOOKAuthor: Otmar Scherzer
Publisher: Springer Science & Business Media
Published: 2010-11-23
Total Pages: 1626
ISBN-13: 0387929193
DOWNLOAD EBOOKThe Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.
