Functional Analysis

e-books in Functional Analysis category

Fredholm Operators and Spectral Flow
by - arXiv ,
Fredholm operators are one of the most important classes of linear operators in mathematics. The aim of these notes is an essentially self-contained introduction to the spectral flow for paths of (generally unbounded) selfadjoint Fredholm operators.
(5970 views)
Banach Spaces of Analytic Functions
by - Prentice-Hall ,
A classic of pure mathematics, this advanced text explores the intersection of functional analysis and analytic function theory. Close in spirit to abstract harmonic analysis, it is confined to Banach spaces of analytic functions in the unit disc.
(7512 views)

Functional Analysis with Applications
by - arXiv ,
This book at the beginning graduate level will help students with primary interests elsewhere to acquire a facility with tools of a functional analytic flavor, say in harmonic analysis, numerical analysis, stochastic processes, or in physics.
(9794 views)
Lectures on Cyclic Homology
by - Tata Institute of Fundamental Research ,
Contents: Exact Couples and the Connes Exact Couple; Abelianization and Hochschild Homology; Cyclic Homology and the Connes Exact Couple; Cyclic Homology and Lie Algebra Homology; Mixed Complexes, the Connes Operator B; and more.
(8234 views)
Operators on Hilbert Space
by - King's College London ,
These are notes for a King's College course to fourth year undergraduates and MSc students. They cover the theoretical development of operators on Hilbert space up to the spectral theorem for bounded selfadjoint operators.
(8520 views)
C*-algebraic Methods in Spectral Theory
by - Nagoya University ,
From the table of contents: Linear operators on a Hilbert space; C*-algebras; Crossed product C*-algebras; Schroedinger operators and essential spectrum; Twisted crossed product C*-algebras; Pseudodifferential calculus; Magnetic systems.
(8372 views)
C*-algebras
by - King's College, London ,
These notes form an introductory account of C*-algebras. Some results on more general commutative Banach algebras, whose proofs require little extra effort, are included. There are accounts of two applications of the commutative theory ...
(9206 views)
Basic Analysis Gently Done: Topological Vector Spaces
by - King's College, London ,
These notes are based on lectures given as part of a mathematics MSc program. The approach here is to discuss topological vector spaces - with normed spaces considered as special cases. Contents: Topological Spaces; Nets; Product Spaces; etc.
(9517 views)
Functional Analysis
by - Lancaster University ,
These lecture notes are an expanded version of a set written for a course given to final-year undergraduates at the University of Oxford. A thorough understanding of Banach and Hilbert spaces is a prerequisite for this material.
(11221 views)
Banach Modules and Functors on Categories of Banach Spaces
by - Marcel Dekker Inc ,
This book is the final outgrowth of a sequence of seminars about functors on categories of Banach spaces (held 1971 - 1975) and several doctoral dissertations. It has been written for readers with a general background in functional analysis.
(9687 views)
Functors and Categories of Banach Spaces
by - Springer ,
The aim of this book is to develop the theory of Banach operator ideals and metric tensor products along categorical lines: these two classes of mathematical objects are endofunctors on the category Ban of all Banach spaces in a natural way.
(9631 views)
Functional Analysis
by - arXiv ,
Notes from a course which covered themes in functional analysis and operator theory, with an emphasis on topics of special relevance to such applications as representation theory, harmonic analysis, mathematical physics, and stochastic integration.
(11109 views)
Lectures On Some Fixed Point Theorems Of Functional Analysis
by - Tata Institute Of Fundamental Research ,
The book is concerned with the application of a variety of methods to both non-linear (fixed point) problems and linear (eigenvalue) problems in infinite dimensional spaces. Author was interested in the construction of eigenvectors and eigenvalues.
(9533 views)
Distribution Theory (Generalized Functions)
by ,
From the table of contents: Introduction; The spaces S and S'; The spaces D and D'; The Fourier transform; Convolution; Fourier-Laplace Transform; Structure Theorem for Distributions; Partial Differential Equations; and more.
(9938 views)
Functional Analysis Lecture Notes
by - University of East Anglia ,
Lecture notes for a 3rd year undergraduate course in functional analysis. By the end of the course, you should have a good understanding of normed vector spaces, Hilbert and Banach spaces, fixed point theorems and examples of function spaces.
(10242 views)
Introduction to Functional Analysis
by - University of Leeds ,
Contents: Fourier Series; Basics of Linear Spaces; Orthogonality; Fourier Analysis; Duality of Linear Spaces; Operators; Spectral Theory; Compactness; The spectral theorem for compact normal operators; Applications to integral equations; etc.
(11917 views)
Special Course in Functional Analysis: (Non-)Commutative Topology
by - Aalto TKK ,
In this book you will learn something about functional analytic framework of topology. And you will get an access to more advanced literature on non-commutative geometry, a quite recent topic in mathematics and mathematical physics.
(10265 views)
Notes on Operator Algebras
by - Los Alamos National Laboratory ,
Lecture notes on operator algebras. From the table of contents: Structure Theory I; von Neumann Algebras; States and Representations; Structure Theory II; Matrices; Automorphism Groups; Extensions; K-Theory; Nuclear C* Algebras.
(10167 views)
Lecture notes on C*-algebras, Hilbert C*-modules, and quantum mechanics
by - arXiv ,
A graduate-level introduction to C*-algebras, Hilbert C*-modules, vector bundles, and induced representations of groups and C*-algebras, with applications to quantization theory, phase space localization, and configuration space localization.
(11731 views)
Integral Operators
by - BookBoon ,
Examples of Hilbert-Smith operators and other types of integral operators, Hilbert Schmidt norm, Volterra integral operator, Cauchy-Schwarz inequality, Hoelder inequality, iterated kernels, Hermitian kernel, and much more.
(11007 views)
Spectral Theory
by - BookBoon ,
Spectral Theory - Functional Analysis Examples. Contents: Spectrum and resolvent; The adjoint of a bounded operator; Self adjoint operator; Isometric operators; Unitary and normal operators; Positive operators and projections; Compact operators.
(12025 views)
Hilbert Spaces and Operators on Hilbert Spaces
by - BookBoon ,
Functional analysis examples. From the table of contents: Hilbert spaces; Fourier series; Construction of Hilbert spaces; Orthogonal projections and complements; Weak convergence; Operators on Hilbert spaces, general; Closed operations.
(11326 views)
Global Analysis: Functional Analysis Examples
by - BookBoon ,
From the table of contents: Metric spaces; Topology; Continuous mappings; Sequences; Semi-continuity; Connected sets, differentiation; Normed vector spaces and integral operators; Differentiable mappings; Complete metric spaces; and more.
(11851 views)
Von Neumann Algebras
by - UC Berkeley Mathematics ,
The purpose of these notes is to provide a rapid introduction to von Neumann algebras which gets to the examples and active topics with a minimum of technical baggage. The philosophy is to lavish attention on a few key results and examples.
(12596 views)
Nonlinear Functional Analysis
by - University of Vienna ,
This manuscript provides a brief introduction to nonlinear functional analysis. As an application we consider partial differential equations and prove existence and uniqueness for solutions of the stationary Navier-Stokes equation.
(13438 views)
Functional Analysis
by - University of Vienna ,
This free manuscript provides a brief introduction to Functional Analysis. The text covers basic Hilbert and Banach space theory including Lebesgue spaces and their duals (no knowledge about Lebesgue integration is assumed).
(12742 views)
Topics in Real and Functional Analysis
by - Universitaet Wien ,
This manuscript provides a brief introduction to Real and (linear and nonlinear) Functional Analysis. It covers basic Hilbert and Banach space theory as well as basic measure theory including Lebesgue spaces and the Fourier transform.
(13871 views)
Operator Algebras and Quantum Statistical Mechanics
by - Springer ,
These two volumes present the theory of operator algebras with applications to quantum statistical mechanics. The authors' approach to the operator theory is to a large extent governed by the dictates of the physical applications.
(16924 views)
Linear Functional Analysis
by - Macquarie University ,
An introduction to the basic ideas in linear functional analysis: metric spaces; connectedness, completeness and compactness; normed vector spaces; inner product spaces; orthogonal expansions; linear functionals; linear transformations; etc.
(14837 views)
Jordan Operator Algebras
by - Pitman ,
Introduction to Jordan algebras of operators on Hilbert spaces and their abstract counterparts. It develops the theory of Jordan operator algebras to a point from which the theory of C*- and von Neumann algebras can be generalized to Jordan algebras.
(12547 views)
Hilbert Space Methods for Partial Differential Equations
by - Pitman ,
Written for beginning graduate students of mathematics, engineering, and the physical sciences. It covers elements of Hilbert space, distributions and Sobolev spaces, boundary value problems, first order evolution equations, etc.
(14828 views)