Elliptic Operators Topology And Asymptotic Methods
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Elliptic Operators Topology And Asymptotic Methods
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Author : John Roe
language : en
Publisher: CRC Press
Release Date : 2013-12-19
Elliptic Operators Topology And Asymptotic Methods written by John Roe and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-19 with Mathematics categories.
Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important exampl
Elliptic Operators Topology And Asymptotic Methods
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Author : John Roe
language : en
Publisher: Longman Scientific and Technical
Release Date : 1988
Elliptic Operators Topology And Asymptotic Methods written by John Roe and has been published by Longman Scientific and Technical this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Geometric And Topological Invariants Of Elliptic Operators
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Author : Jerome Kaminker
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Geometric And Topological Invariants Of Elliptic Operators written by Jerome Kaminker and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
This volume contains the proceedings of the AMS-IMS-SIAM Summer Research Conference on ``Geometric and Topological Invariants of Elliptic Operators,'' held in August 1988 at Bowdoin College. Some of the themes covered at the conference and appearing in the articles are: the use of more sophisticated asymptotic methods to obtain index theorems, the study of the $\eta$ invariant and analytic torsion, and index theory on open manifolds and foliated manifolds. The current state of noncommutative differential geometry, as well as operator algebraic and $K$-theoretic methods, are also presented in several the articles. This book will be useful to researchers in index theory, operator algebras, foliations, and mathematical physics. Topologists and geometers are also likely to find useful the view the book provides of recent work in this area. In addition, because of the expository nature of several of the articles, it will be useful to graduate students interested in working in these areas.
Functional Analytic Methods For Heat Green Operators
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Author : Kazuaki Taira
language : en
Publisher: Springer Nature
Release Date : 2024-09-18
Functional Analytic Methods For Heat Green Operators written by Kazuaki Taira and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-18 with Mathematics categories.
This monograph guides the reader to the mathematical crossroads of heat equations and differential geometry via functional analysis. Following the recent trend towards constructive methods in the theory of partial differential equations, it makes extensive use of the ideas and techniques from the Weyl–Hörmander calculus of pseudo-differential operators to study heat Green operators through concrete calculations for the Dirichlet, Neumann, regular Robin and hypoelliptic Robin boundary conditions. Further, it provides detailed coverage of important examples and applications in elliptic and parabolic problems, illustrated with many figures and tables. A unified mathematical treatment for solving initial boundary value problems for the heat equation under general Robin boundary conditions is desirable, and leads to an extensive study of various aspects of elliptic and parabolic partial differential equations. The principal ideas are explicitly presented so that a broad spectrum of readers can easily understand the problem and the main results. The book will be of interest to readers looking for a functional analytic introduction to the meeting point of partial differential equations, differential geometry and probability.
Geometric Methods In Physics
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Author : Piotr Kielanowski
language : en
Publisher: Birkhäuser
Release Date : 2015-09-21
Geometric Methods In Physics written by Piotr Kielanowski and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-21 with Mathematics categories.
This book presents a selection of papers based on the XXXIII Białowieża Workshop on Geometric Methods in Physics, 2014. The Białowieża Workshops are among the most important meetings in the field and attract researchers from both mathematics and physics. The articles gathered here are mathematically rigorous and have important physical implications, addressing the application of geometry in classical and quantum physics. Despite their long tradition, the workshops remain at the cutting edge of ongoing research. For the last several years, each Białowieża Workshop has been followed by a School on Geometry and Physics, where advanced lectures for graduate students and young researchers are presented; some of the lectures are reproduced here. The unique atmosphere of the workshop and school is enhanced by its venue, framed by the natural beauty of the Białowieża forest in eastern Poland. The volume will be of interest to researchers and graduate students in mathematical physics, theoretical physics and mathematmtics.
Index Theory And Operator Algebras
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Author : Jeffrey Stephen Fox
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Index Theory And Operator Algebras written by Jeffrey Stephen Fox and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
This collection of papers by leading researchers provides a broad picture of current research directions in index theory. Based on lectures presented at the NSF-CBMS Regional Conference on $K$-Homology and Index Theory, held in August, 1991 at the University of Colorado at Boulder, the book provides both a careful exposition of new perspectives in classical index theory and an introduction to currently active areas of the field. Presented here are two new proofs of the classical Atiyah-Singer Index Theorem, as well as index theorems for manifolds with boundary and open manifolds. Index theory for semi-simple $p$-adic groups and the geometry of discrete groups are also discussed. Throughout the book, the application of operator algebras emerges as a central theme. Aimed at graduate students and researchers, this book is suitable as a text for an advanced graduate course on index theory.
The Atiyah Patodi Singer Index Theorem
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Author : Richard Melrose
language : en
Publisher: CRC Press
Release Date : 1993-03-31
The Atiyah Patodi Singer Index Theorem written by Richard Melrose and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-03-31 with Mathematics categories.
Based on the lecture notes of a graduate course given at MIT, this sophisticated treatment leads to a variety of current research topics and will undoubtedly serve as a guide to further studies.
S Minaire De Probabilit S Xxxvi
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Author : Jacques Azéma
language : en
Publisher: Springer
Release Date : 2004-10-21
S Minaire De Probabilit S Xxxvi written by Jacques Azéma and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-21 with Mathematics categories.
The 36th Sminaire de Probabilits contains an advanced course on Logarithmic Sobolev Inequalities by A. Guionnet and B. Zegarlinski, as well as two shorter surveys by L. Pastur and N. O'Connell on the theory of random matrices and their links with stochastic processes. The main themes of the other contributions are Logarithmic Sobolev Inequalities, Stochastic Calculus, Martingale Theory and Filtrations. Besides the traditional readership of the Sminaires, this volume will be useful to researchers in statistical mechanics and mathematical finance.
Perspectives On Noncommutative Geometry
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Author : Masoud Khalkhali
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Perspectives On Noncommutative Geometry written by Masoud Khalkhali and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
This volume represents the proceedings of the Noncommutative Geometry Workshop that was held as part of the thematic program on operator algebras at the Fields Institute in May 2008. Pioneered by Alain Connes starting in the late 1970s, noncommutative geometry was originally inspired by global analysis, topology, operator algebras, and quantum physics. Its main applications were to settle some long-standing conjectures, such as the Novikov conjecture and the Baum-Connes conjecture. Next came the impact of spectral geometry and the way the spectrum of a geometric operator, like the Laplacian, holds information about the geometry and topology of a manifold, as in the celebrated Weyl law. This has now been vastly generalized through Connes' notion of spectral triples. Finally, recent years have witnessed the impact of number theory, algebraic geometry and the theory of motives, and quantum field theory on noncommutative geometry. Almost all of these aspects are touched upon with new results in the papers of this volume. This book is intended for graduate students and researchers in both mathematics and theoretical physics who are interested in noncommutative geometry and its applications.
Old And New Aspects In Spectral Geometry
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Author : M.-E. Craioveanu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Old And New Aspects In Spectral Geometry written by M.-E. Craioveanu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
It is known that to any Riemannian manifold (M, g ) , with or without boundary, one can associate certain fundamental objects. Among them are the Laplace-Beltrami opera tor and the Hodge-de Rham operators, which are natural [that is, they commute with the isometries of (M,g)], elliptic, self-adjoint second order differential operators acting on the space of real valued smooth functions on M and the spaces of smooth differential forms on M, respectively. If M is closed, the spectrum of each such operator is an infinite divergent sequence of real numbers, each eigenvalue being repeated according to its finite multiplicity. Spectral Geometry is concerned with the spectra of these operators, also the extent to which these spectra determine the geometry of (M, g) and the topology of M. This problem has been translated by several authors (most notably M. Kac). into the col loquial question "Can one hear the shape of a manifold?" because of its analogy with the wave equation. This terminology was inspired from earlier results of H. Weyl. It is known that the above spectra cannot completely determine either the geometry of (M , g) or the topology of M. For instance, there are examples of pairs of closed Riemannian manifolds with the same spectra corresponding to the Laplace-Beltrami operators, but which differ substantially in their geometry and which are even not homotopically equiva lent.