Fredholm Theory In Banach Spaces

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Fredholm Theory In Banach Spaces

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Author : Anthony Francis Ruston
language : en
Publisher: Cambridge University Press
Release Date : 2004-06-03

Fredholm Theory In Banach Spaces written by Anthony Francis Ruston and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-03 with Mathematics categories.

Presents analogues for operators on Banach spaces of Fredholm's solution of integral equations of the second kind.

The Fredholm Theory In Banach Spaces

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Author : Robert Lawrence Graves
language : en
Publisher:
Release Date : 1952

The Fredholm Theory In Banach Spaces written by Robert Lawrence Graves and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1952 with categories.

Fredholm And Local Spectral Theory With Applications To Multipliers

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Author : Pietro Aiena
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-08

Fredholm And Local Spectral Theory With Applications To Multipliers written by Pietro Aiena 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 2007-05-08 with Mathematics categories.

A signi?cant sector of the development of spectral theory outside the classical area of Hilbert space may be found amongst at multipliers de?ned on a complex commutative Banach algebra A. Although the general theory of multipliers for abstract Banach algebras has been widely investigated by several authors, it is surprising how rarely various aspects of the spectral theory, for instance Fredholm theory and Riesz theory, of these important classes of operators have been studied. This scarce consideration is even more surprising when one observes that the various aspects of spectral t- ory mentioned above are quite similar to those of a normal operator de?ned on a complex Hilbert space. In the last ten years the knowledge of the spectral properties of multip- ers of Banach algebras has increased considerably, thanks to the researches undertaken by many people working in local spectral theory and Fredholm theory. This research activity recently culminated with the publication of the book of Laursen and Neumann [214], which collects almost every thing that is known about the spectral theory of multipliers.

Polyfold And Fredholm Theory

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Author : Helmut Hofer
language : en
Publisher: Springer Nature
Release Date : 2021-07-21

Polyfold And Fredholm Theory written by Helmut Hofer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-21 with Mathematics categories.

This book pioneers a nonlinear Fredholm theory in a general class of spaces called polyfolds. The theory generalizes certain aspects of nonlinear analysis and differential geometry, and combines them with a pinch of category theory to incorporate local symmetries. On the differential geometrical side, the book introduces a large class of `smooth’ spaces and bundles which can have locally varying dimensions (finite or infinite-dimensional). These bundles come with an important class of sections, which display properties reminiscent of classical nonlinear Fredholm theory and allow for implicit function theorems. Within this nonlinear analysis framework, a versatile transversality and perturbation theory is developed to also cover equivariant settings. The theory presented in this book was initiated by the authors between 2007-2010, motivated by nonlinear moduli problems in symplectic geometry. Such problems are usually described locally as nonlinear elliptic systems, and they have to be studied up to a notion of isomorphism. This introduces symmetries, since such a system can be isomorphic to itself in different ways. Bubbling-off phenomena are common and have to be completely understood to produce algebraic invariants. This requires a transversality theory for bubbling-off phenomena in the presence of symmetries. Very often, even in concrete applications, geometric perturbations are not general enough to achieve transversality, and abstract perturbations have to be considered. The theory is already being successfully applied to its intended applications in symplectic geometry, and should find applications to many other areas where partial differential equations, geometry and functional analysis meet. Written by its originators, Polyfold and Fredholm Theory is an authoritative and comprehensive treatise of polyfold theory. It will prove invaluable for researchers studying nonlinear elliptic problems arising in geometric contexts.

Handbook Of The Geometry Of Banach Spaces

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Author :
language : en
Publisher: Elsevier
Release Date : 2001-08-15

Handbook Of The Geometry Of Banach Spaces written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-15 with Mathematics categories.

The Handbook presents an overview of most aspects of modernBanach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banachspace theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory.

Spectral Theory Of Bounded Linear Operators

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Author : Carlos S. Kubrusly
language : en
Publisher: Springer Nature
Release Date : 2020-01-30

Spectral Theory Of Bounded Linear Operators written by Carlos S. Kubrusly and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-30 with Mathematics categories.

This textbook introduces spectral theory for bounded linear operators by focusing on (i) the spectral theory and functional calculus for normal operators acting on Hilbert spaces; (ii) the Riesz-Dunford functional calculus for Banach-space operators; and (iii) the Fredholm theory in both Banach and Hilbert spaces. Detailed proofs of all theorems are included and presented with precision and clarity, especially for the spectral theorems, allowing students to thoroughly familiarize themselves with all the important concepts. Covering both basic and more advanced material, the five chapters and two appendices of this volume provide a modern treatment on spectral theory. Topics range from spectral results on the Banach algebra of bounded linear operators acting on Banach spaces to functional calculus for Hilbert and Banach-space operators, including Fredholm and multiplicity theories. Supplementary propositions and further notes are included as well, ensuring a wide range of topics in spectral theory are covered. Spectral Theory of Bounded Linear Operators is ideal for graduate students in mathematics, and will also appeal to a wider audience of statisticians, engineers, and physicists. Though it is mostly self-contained, a familiarity with functional analysis, especially operator theory, will be helpful.

Geometric Harmonic Analysis Ii

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Author : Dorina Mitrea
language : en
Publisher: Springer Nature
Release Date : 2023-03-03

Geometric Harmonic Analysis Ii written by Dorina Mitrea and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-03 with Mathematics categories.

This monograph is part of a larger program, materializing in five volumes, whose principal aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. Volume II is concerned with function spaces measuring size and/or smoothness, such as Hardy spaces, Besov spaces, Triebel-Lizorkin spaces, Sobolev spaces, Morrey spaces, Morrey-Campanato spaces, spaces of functions of Bounded Mean Oscillations, etc., in general geometric settings. Work here also highlights the close interplay between differentiability properties of functions and singular integral operators. The text is intended for researchers, graduate students, and industry professionals interested in harmonic analysis, functional analysis, geometric measure theory, and function space theory.

Fredholm And Local Spectral Theory Ii

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Author : Pietro Aiena
language : en
Publisher: Springer
Release Date : 2018-11-24

Fredholm And Local Spectral Theory Ii written by Pietro Aiena and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-24 with Mathematics categories.

This monograph concerns the relationship between the local spectral theory and Fredholm theory of bounded linear operators acting on Banach spaces. The purpose of this book is to provide a first general treatment of the theory of operators for which Weyl-type or Browder-type theorems hold. The product of intensive research carried out over the last ten years, this book explores for the first time in a monograph form, results that were only previously available in journal papers. Written in a simple style, with sections and chapters following an easy, natural flow, it will be an invaluable resource for researchers in Operator Theory and Functional Analysis. The reader is assumed to be familiar with the basic notions of linear algebra, functional analysis and complex analysis.

Encyclopaedia Of Mathematics

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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 1989-08-31

Encyclopaedia Of Mathematics written by Michiel Hazewinkel 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 1989-08-31 with Mathematics categories.

V.1. A-B v.2. C v.3. D-Feynman Measure. v.4. Fibonaccimethod H v.5. Lituus v.6. Lobachevskii Criterion (for Convergence)-Optical Sigman-Algebra. v.7. Orbi t-Rayleigh Equation. v.8. Reaction-Diffusion Equation-Stirling Interpolation Fo rmula. v.9. Stochastic Approximation-Zygmund Class of Functions. v.10. Subject Index-Author Index.

A Short Course On Spectral Theory

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Author : William Arveson
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18

A Short Course On Spectral Theory written by William Arveson 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 2006-04-18 with Mathematics categories.

This book presents the basic tools of modern analysis within the context of what might be called the fundamental problem of operator theory: to calculate spectra of specific operators on infinite-dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more refined methods that allow one to approach problems that go well beyond the computation of spectra; the mathematical foundations of quantum physics, noncommutative K-theory, and the classification of simple C-algebras being three areas of current research activity that require mastery of the material presented here. The notion of spectrum of an operator is based on the more abstract notion of the spectrum of an element of a complex Banach algebra. After working out these fundamentals we turn to more concrete problems of computing spectra of operators of various types. For normal operators, this amounts to a treatment of the spectral theorem. Integral operators require 2 the development of the Riesz theory of compact operators and the ideal L of Hilbert–Schmidt operators. Toeplitz operators require several important tools; in order to calculate the spectra of Toeplitz operators with continuous symbol one needs to know the theory of Fredholm operators and index, the ? structure of the Toeplitz C-algebra and its connection with the topology of curves, and the index theorem for continuous symbols.