Functional analysis and transforms

This specialized and authoritative book contains an overview of modern approaches to constructing approximations to solutions of ill-posed operator equations, both linear and nonlinear.

The aim of this book is to provide a concise but complete introduction to the main mathematical tools of nonlinear functional analysis, which are also used in the study of concrete problems in economics, engineering, and physics.

With applications in quantum field theory, general relativity and elementary particle physics, this four-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras.

With applications in quantum field theory, general relativity and elementary particle physics, this four-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras.

This book extends classical Hermite-Hadamard type inequalities to the fractional case via establishing fractional integral identities, and discusses Riemann-Liouville and Hadamard integrals, respectively, by various convex functions.

This book extends classical Hermite-Hadamard type inequalities to the fractional case via establishing fractional integral identities, and discusses Riemann-Liouville and Hadamard integrals, respectively, by various convex functions.

This monograph develops the theory of pre-Riesz spaces, which are the partially ordered vector spaces that embed order densely into Riesz spaces.

This monograph develops the theory of pre-Riesz spaces, which are the partially ordered vector spaces that embed order densely into Riesz spaces.

This textbook on functional analysis offers a short and concise introduction to the subject.

This textbook on functional analysis offers a short and concise introduction to the subject.

With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schrodinger algebras, applications to holography.

With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schrodinger algebras, applications to holography.

In this textbook, a concise approach to complex analysis of one and several variables is presented.

In this textbook, a concise approach to complex analysis of one and several variables is presented.

This book is devoted to the analysis of the basic boundary value problems for the Laplace equation in singularly perturbed domains.

The first of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields.

This book is about the subject of higher smoothness in separable real Banach spaces.

This book provides a systematic, rigorous and self-contained treatment of positive dynamical systems.

In the past two decades, convex analysis and optimization have been developed in Hadamard spaces.

This research monograph gives a detailed account of a theory which is mainly concerned with certain classes of degenerate differential operators, Markov semigroups and approximation processes.

This book is the first volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research.

The book is the first systematical treatment of the theory of finite elements in Archimedean vector lattices and contains the results known on this topic up to the year 2013.

The focus of this book is on open conformal dynamical systems corresponding to the escape of a point through an open Euclidean ball.

The monograph gives a detailed exposition of the theory of general elliptic operators (scalar and matrix) and elliptic boundary value problems in Hilbert scales of Hormander function spaces.

This research monograph gives a detailed account of a theory which is mainly concerned with certain classes of degenerate differential operators, Markov semigroups and approximation processes.

This book provides a systematic, rigorous and self-contained treatment of positive dynamical systems.

The book is the first systematical treatment of the theory of finite elements in Archimedean vector lattices and contains the results known on this topic up to the year 2013.

In the past two decades, convex analysis and optimization have been developed in Hadamard spaces.

Elliptic partial differential equations is one of the main and most active areas in mathematics.

The theory of distributions has numerous applications and is extensively used in mathematics, physics and engineering.

The monograph gives a detailed exposition of the theory of general elliptic operators (scalar and matrix) and elliptic boundary value problems in Hilbert scales of Hormander function spaces.

In the last 40 years semi-linear elliptic equations became a central subject of study in the theory of nonlinear partial differential equations.

This book deals with analytic treatments of Markov processes.

This monograph gives a systematic presentation of classical and recent results obtained in the last couple of years.

This monograph aims to give a self-contained introduction into the whole field of topological analysis: Requiring essentially only basic knowledge of elementary calculus and linear algebra, it provides all required background from topology, analysis, linear and nonlinear functional analysis, and multivalued maps, containing even basic topics like separation axioms, inverse and implicit function theorems, the Hahn-Banach theorem, Banach manifolds, or the most important concepts of continuity of multivalued maps.

This monograph contains a study on various function classes, a number of new results and new or easy proofs of old results (Fefferman-Stein theorem on subharmonic behavior, theorems on conjugate functions and fractional integration on Bergman spaces, Fefferman's duality theorem), which are interesting for specialists; applications of the Hardy-Littlewood inequalities on Taylor coefficients to (C, a)-maximal theorems and (C, a)-convergence; a study of BMOA, due to Knese, based only on Green's formula; the problem of membership of singular inner functions in Besov and Hardy-Sobolev spaces; a full discussion of g-function (all p > 0) and Calderon's area theorem; a new proof, due to Astala and Koskela, of the Littlewood-Paley inequality for univalent functions; and new results and proofs on Lipschitz spaces, coefficient multipliers and duality, including compact multipliers and multipliers on spaces with non-normal weights.

In recent years, technological progress created a great need for complex mathematical models.

This book grew out of a course taught in the Department of Mathematics, Indian Institute of Technology, Delhi, which was tailored to the needs of the applied community of mathematicians, engineers, physicists etc.

This book is about the subject of higher smoothness in separable real Banach spaces.

Most classes of operators that are not isomorphic embeddings are characterized by some kind of a "e;smallness"e; condition.

Embeddings of discrete metric spaces into Banach spaces recently became an important tool in computer science and topology.

The aim of this monograph is to give a thorough and self-contained account of functions of (generalized) bounded variation, the methods connected with their study, their relations to other important function classes, and their applications to various problems arising in Fourier analysis and nonlinear analysis.

Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems.

Ill-posed problems are encountered in countless areas of real world science and technology.

This is the first part of the second revised and extended edition of the well established book "e;Function Spaces"e; by Alois Kufner, Oldrich John, and Svatopluk Fucik.

This textbook provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their applications to partial differential equations.

This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev lattice structure, a simple extension of the well-established notion of a chain (or scale) of Hilbert spaces.