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Dirac Operators in Representation Theory
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Jing-Song Huang, Pavle Pandzic
This monograph presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology. Dirac operators are widely used in physics, differential geometry, and group-theoretic settings (particularly, the geometric construction of discrete series representations). The related concept of Dirac cohomology, which is defined ...
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Linear partial differential operators.
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Lars Hörmander
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The Nonlinear Limit-Point/Limit-Circle Problem
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Miroslav Bartisek, Miroslav Bartusek, Zuzana Dosia
First posed by Hermann Weyl in 1910, the limit-point/limit-circle problem has inspired, over the last century, several new developments in the asymptotic analysis of nonlinear differential equations. This self-contained monograph traces the evolution of this problem from its inception to its modern-day extensions to the study of deficiency indices ...
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The Analysis of Linear Partial Differential Operators I: Distribution Theory & Fourier Analysis
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by
L Hormander
Due to popular demand this classic presentation of a vast amount on linear partial differential equations by a consummate master of the subject is now available as a study edition. The main change in this new edition is the inclusion of exercises with answers and hints. That is meant to emphasize that this volume can perfectly serve as a general ...
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Mathematical Aspects of Nonlinear Dispersive Equations
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Jean Bourgain (Editor), Carlos E Kenig (Editor), Sergiu Klainerman (Editor)
This collection of new and original papers on mathematical aspects of nonlinear dispersive equations includes both expository and technical papers that reflect a number of recent advances in the field. The expository papers describe the state of the art and research directions. The technical papers concentrate on a specific problem and the related ...
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Function spaces, entropy numbers, differential operators
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Edmunds, Triebel
The distribution of the eigenvalues of differential operators has long fascinated mathematicians. Advances have shed light upon classical problems in this area, and this book presents a fresh approach, largely based upon the results of the authors. The emphasis here is on a topic of central importance in analysis, namely the relationship between i ...
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Microdifferential Systems in the Complex Domain
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Pierre Schapira
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Fundamental Solutions of Partial Differential Equations and Applications
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by
Prem K Kythe
The main purpose of this book is to provide a self-contained and systematic development of an aspect of analysis which deals with the theory of fundamental solutions for differential operators and their applications to boundary value problems of mathematical physics, applied mathematics, and engineering, with the related computational aspects. A ...
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Microlocal analysis for differential operators an introduction
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Grigis, Sjöstrand
This short introduction to microlocal analysis is presented, in the spirit of Hormander, in the classical framework of partial differential equations. This theory has important applications in areas such as harmonic and complex analysis, and also in theoretical physics. Here Grigis and Sjostrand emphasise the basic tools, especially the method of ...
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Spectral Theory of Linear Differential Operators and Comparison Algebras
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Heinz Otto Cordes, N J Hitchin (Editor)
The main aim of this book is to introduce the reader to the concept of comparison algebra, defined as a type of C*-algebra of singular integral operators. The first part of the book develops the necessary elements of the spectral theory of differential operators as well as the basic properties of elliptic second order differential operators. The ...
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Function Spaces, Differential Operators and Nonlinear Analysis: The Hans Triebel Anniversary Volume
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Dorothee Haroske (Editor), Thomas Runst (Editor), Hans-Juurgen Schmeisser (Editor)
The presented collection of papers is based on lectures given at the International Conference "Function Spaces, Differential Operators and Nonlinear Analysis" (FSDONA-01) held in Teistungen, Thuringia/Germany, from June 28 to July 4, 2001. They deal with the symbiotic relationship between the theory of function spaces, harmonic analysis, linear ...
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Differential Equations with Operator Coefficients: With Applications to Boundary Value Problems for Partial Differential Equations
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Vladimir Kozlov, C Birkenhake, H Lange
This book is the first systematic and self-contained presentation of a theory of arbitrary order ordinary differential equations with unbounded operator coefficients in a Hilbert or Banach space, developed over the last 10 years by the authors. It deals with conditions of solvability, classes of uniqueness, estimates for solutions and asymptotic ...
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Dirac Operators in Analysis
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by
John Ryan, Daniele C Struppa, C C Struppa
Clifford analysis has blossomed into an increasingly relevant and fashionable area of research in mathematical analysis-it fits conveniently at the crossroads of many fundamental areas of research, including classical harmonic analysis, operator theory, and boundary behavior. This book presents a state-of-the-art account of the most recent ...
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Global Calculus
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by
S Ramanan
Analysis, topology and algebra brought new power to geometry, revolutionizing the way geometers and physicists look at conceptual problems. Some of the key ingredients in this interplay are sheaves, cohomology, Lie groups, connections and differential operators. In "Global Calculus", the appropriate formalism for these topics is laid out with ...
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Applied Analysis by the Hilbert Space Method: An Introduction with Applications to the Wave, Heat, and Schrodinger Equations
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by
Samuel S Holland
Numerous examples and exercises highlight this unified treatment of the Hermitian operator theory in its Hilbert space setting. Its simple explanations of difficult subjects make it intuitively appealing to students in applied mathematics, physics, and engineering. It is also a fine reference for professionals. 1990 edition.
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Differentiability of Six Operators on Nonsmooth Functions and P-Variation
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by
Richard M Dudley, Rimas Norvaisa, J Qian (Contributions by)
The book is about differentiability of six operators on functions or pairs of functions: composition (f of g), integration (of f dg), multiplication and convolution of two functions, both varying, and the product integral and inverse operators for one function. The operators are differentiable with respect to p-variation norms with optimal ...
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Sturm-Liouville Theory: Past and Present
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by
Werner Amrein (Editor), David Pearson (Editor), Andreas Hinz (Editor)
This is a collection of survey articles based on lectures presented at a colloquium and workshop in Geneva in 2003 to commemorate the 200th anniversary of the birth of Charles Francois Sturm. It aims at giving an overview of the development of Sturm-Liouville theory from its historical roots to present day research. It is the first time that such ...
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The Neumann Problem for the Cauchy-Riemann Complex
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by
G. B. Folland, J. J. Kohn
This book is based on the notes from lectures given by the second author at Princeton University in the year 1970-71, which were subsequently expanded and revised by the first author.
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Spectral theory and differential operators
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by
Edmunds, Evans 1940-
This book contains an up-to-date account of those parts of the theory of bounded and closed linear operators in Banach and Hilbert spaces relevant to spectral problems involving differential equations. The main themes are essential spectra, measures of non-compactness, entropy numbers, approximation numbers, eigenvalues and their ...
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Asymptototic Distribution of Eigenvalues of Differential Operators
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Serge Levendorskii
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Dirac Operators and Spectral Geometry
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Giampiero Esposito, Peter Goddard (Editor), Julia Yeomans (Editor)
The Dirac operator has many useful applications in theoretical physics and mathematics. This book provides a clear, concise and self-contained introduction to the global theory of the Dirac operator and to the analysis of spectral asymptotics with local or non-local boundary conditions. The theory is introduced at a level suitable for graduate ...
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Invariance theory, the heat equation, and the Atiyah-Singer index theorem
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by
Peter B Gilkey
This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a manifold with smooth boundary. ...
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G-Convergence and Homogenization of Nonlinear Partial Differential Operators
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by
Alexander A Pankov
This volume deals with G-convergence and homogenization for various classes of nonlinear partial differential operators. Chapter 1 is devoted to some preliminary issues from nonlinear analysis as well as to G-convergence of abstract operators, including the case of abstract parabolic operators. Chapter 2 introduces details of the notion of strong ...
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Analysis on Real & Complex Manifolds
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by
Raghavan Narasimhan
Chapter 1 presents theorems on differentiable functions often used in differential topology, such as the implicit function theorem, Sard's theorem and Whitney's approximation theorem. The next chapter is an introduction to real and complex manifolds. It contains an exposition of the theorem of Frobenius, the lemmata of Poincare and Grothendieck ...
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Spectral Theory and Differential Equations
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by
W N Everitt (Editor)
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