Автор: Adams Название: Function Spaces and Potential Theory ISBN: 3540570608 ISBN-13(EAN): 9783540570608 Издательство: Springer Рейтинг: Цена: 10449 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The subject of this book is the interplay between function space theory and potential theory. A crucial step in classical potential theory is the identification of
the potential energy of a charge with the square of a Hilbert space norm. This leads to the Dirichlet space of locally integrable functions whose gradients are square
More recently, a generalized potential theory has been developed, which has an analogous relationship to the standard Banach function spaces, Sobolev spaces,
Besov spaces etc., that appear naturally in the study of partial differential equations. A surprisingly large part of classical potential theory has been extended to this nonlinear setting. The
extensions are sometimes surprising, usually they are nontrivial and have required new methods.
Автор: Edmunds David E., Evans W. Desmond Название: Hardy Operators, Function Spaces and Embeddings ISBN: 3540219722 ISBN-13(EAN): 9783540219729 Издательство: Springer Рейтинг: Цена: 10449 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to be indispensible in the study of partial differential equations and variational problems. Many developments of the basic theory since its inception arise in response to concrete problems, for example, with the (ubiquitous) sets with fractal boundaries.The theory will probably enjoy substantial further growth, but even now a connected account of the mature parts of it makes a useful addition to the literature. Accordingly, the main themes of this book are Banach spaces and spaces of Sobolev type based on them; integral operators of Hardy type on intervals and on trees; and the distribution of the approximation numbers (singular numbers in the Hilbert space case) of embeddings of Sobolev spaces based on generalised ridged domains.This timely book will be of interest to all those concerned with the partial differential equations and their ramifications. A prerequisite for reading it is a good graduate course in real analysis.
Описание: Over the past several decades, the territory of preserver problems has been continuously enlarging within the frame of linear analysis. The aim of this work is to present a sort of cross-section of the modern theory of preservers on infinite dimensional spaces (operator spaces and function spaces) through the author's corresponding results. Special emphasis is put on preserver problems concerning some structures of Hilbert space operators which appear in quantum mechanics. Moreover, local automorphisms and local isometries of operator algebras and function algebras are discussed in details.
Описание: The papers contained in this book address problems in one and several complex variables. The main theme is the extension of geometric function theory
methods and theorems to several complex variables. The papers present various results on the growth of mappings in various classes as well as observations about the boundary
behavior of mappings, via developing and using some semi group methods.
Описание: This book provides an introduction to complex analysis in several variables. The viewpoint of integral representation theory together with Grauert's bumping method offers a natural extension of single variable techniques to several variables analysis and leads rapidly to important global results. Applications focus on global extension problems for CR functions, such as the Hartogs-Bochner phenomenon and removable singularities for CR functions. Three appendices on differential manifolds, sheaf theory and functional analysis make the book self-contained. Each chapter begins with a detailed abstract, clearly demonstrating the structure and relations of following chapters. New concepts are clearly defined and theorems and propositions are proved in detail. Historical notes are also provided at the end of each chapter. Clear and succinct, this book will appeal to post-graduate students, young researchers seeking an introduction to holomorphic function theory in several variables and lecturers seeking a concise book on the subject.
Описание: Semismooth Newton methods are a modern class of remarkably powerful and versatile algorithms for solving constrained optimization problems with partial differential equations (PDEs), variational inequalities and related problems. This book provides a comprehensive presentation of these methods in function spaces, choosing a balance between thoroughly developed theory and numerical applications. Although largely self-contained, the book also covers recent developments such as state-constrained problems and offers new material on topics such as improved mesh independence results. The theory and methods are applied to a range of practically important problems, including: • optimal control of nonlinear elliptic differential equations • obstacle problems • flow control of instationary Navier–Stokes fluids In addition, the author covers adjoint-based derivative computation and the efficient solution of Newton systems by multigrid and preconditioned iterative methods.
Описание: Potential Function Methods For Approximately Solving Linear Programming Problems breaks new ground in linear programming theory. The book draws on the research developments in three broad areas: linear and integer programming, numerical analysis, and the computational architectures which enable speedy, high-level algorithm design. During the last ten years, a new body of research within the field of optimization research has emerged, which seeks to develop good approximation algorithms for classes of linear programming problems. This work both has roots in fundamental areas of mathematical programming and is also framed in the context of the modern theory of algorithms. The result of this work, in which Daniel Bienstock has been very much involved, has been a family of algorithms with solid theoretical foundations and with growing experimental success. This book will examine these algorithms, starting with some of the very earliest examples, and through the latest theoretical and computational developments.
Автор: Shoikhet D. Название: Semigroups in Geometrical Function Theory ISBN: 0792371119 ISBN-13(EAN): 9780792371113 Издательство: Springer Рейтинг: Цена: 10449 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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) function spaces on Euclidean n-space and on domains; ii) entropy numbers in quasi-Banach spaces; and iii) the distribution of the eigenvalues of degenerate elliptic (pseudo) differential operators. The treatment is largely self-contained and accessible to non-specialists. Both experts and newcomers alike will welcome this unique exposition.
Описание: This volume constitutes the proceedings of the Sixth Conference on Function Spaces, held in Wroclaw, Poland, in September 2001. It discusses the following
topics: convex analysis; operator theory; interpolation theory; theory of real functions; theory of analytic functions; bifurcation theory; Fourier analysis; functional analysis; measure the
ry; geometry of Banach spaces; and the history of mathematics.
Автор: Bosq Название: Linear Processes in Function Spaces ISBN: 0387950524 ISBN-13(EAN): 9780387950525 Издательство: Springer Рейтинг: Цена: 15674 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Discusses linear processes in Banach spaces. This book is useful for statistical researchers interested in functional data analysis.
Описание: Provides an introduction to the theory of analytic functions of a single complex variable. Starting from basic definitions, this text develops the ideas of complex analysis. Each chapter concludes with a selection of exercises.
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