David Eric Edmunds's Books

Hardy Operators, Function Spaces and Embeddings

By: David E. Edmunds,William D. Evans

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Hardy Operators, Function Spaces and Embeddings

By: David E. Edmunds,William D. Evans

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.

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Page Count

334

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662077310

ISBN 13

9783662077313

Spectral Theory and Differential Operators

By: David Eric Edmunds,W. D. Evans

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Spectral Theory and Differential Operators

By: David Eric Edmunds,W. D. Evans

This book is an updated version of the classic 1987 monograph "Spectral Theory and Differential Operators".The original book was a cutting edge account of the theory of bounded and closed linear operators in Banach and Hilbert spaces relevant to spectral problems involving differential equations. It is accessible to a graduate student as well as meeting the needs of seasoned researchers in mathematics and mathematical physics. This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.

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Page Count

610

Publisher

Oxford University Press

Published Date

ISBN 10

0198812051

ISBN 13

9780198812050

Bounded and Compact Integral Operators

By: David E. Edmunds,V.M Kokilashvili,Alexander Meskhi

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Bounded and Compact Integral Operators

By: David E. Edmunds,V.M Kokilashvili,Alexander Meskhi

The monograph presents some of the authors' recent and original results concerning boundedness and compactness problems in Banach function spaces both for classical operators and integral transforms defined, generally speaking, on nonhomogeneous spaces. Itfocuses onintegral operators naturally arising in boundary value problems for PDE, the spectral theory of differential operators, continuum and quantum mechanics, stochastic processes etc. The book may be considered as a systematic and detailed analysis of a large class of specific integral operators from the boundedness and compactness point of view. A characteristic feature of the monograph is that most of the statements proved here have the form of criteria. These criteria enable us, for example, togive var ious explicit examples of pairs of weighted Banach function spaces governing boundedness/compactness of a wide class of integral operators. The book has two main parts. The first part, consisting of Chapters 1-5, covers theinvestigation ofclassical operators: Hardy-type transforms, fractional integrals, potentials and maximal functions. Our main goal is to give a complete description of those Banach function spaces in which the above-mentioned operators act boundedly (com pactly). When a given operator is not bounded (compact), for example in some Lebesgue space, we look for weighted spaces where boundedness (compact ness) holds. We develop the ideas and the techniques for the derivation of appropriate conditions, in terms of weights, which are equivalent to bounded ness (compactness).

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Page Count

655

Publisher

Springer Science & Business Media

Published Date

ISBN 10

940159922X

ISBN 13

9789401599221

Representations of Linear Operators Between Banach Spaces

By: David E. Edmunds,W. Desmond Evans

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Representations of Linear Operators Between Banach Spaces

By: David E. Edmunds,W. Desmond Evans

The book deals with the representation in series form of compact linear operators acting between Banach spaces, and provides an analogue of the classical Hilbert space results of this nature that have their roots in the work of D. Hilbert, F. Riesz and E. Schmidt. The representation involves a recursively obtained sequence of points on the unit sphere of the initial space and a corresponding sequence of positive numbers that correspond to the eigenvectors and eigenvalues of the map in the Hilbert space case. The lack of orthogonality is partially compensated by the systematic use of polar sets. There are applications to the p-Laplacian and similar nonlinear partial differential equations. Preliminary material is presented in the first chapter, the main results being established in Chapter 2. The final chapter is devoted to the problems encountered when trying to represent non-compact maps.

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Page Count

164

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3034806426

ISBN 13

9783034806428

Differential Operators On Spaces Of Variable Integrability

By: Osvaldo Mendez,Jan Lang,David E Edmunds

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Differential Operators On Spaces Of Variable Integrability

By: Osvaldo Mendez,Jan Lang,David E Edmunds

The theory of Lebesgue and Sobolev spaces with variable integrability is experiencing a steady expansion, and is the subject of much vigorous research by functional analysts, function-space analysts and specialists in nonlinear analysis. These spaces have attracted attention not only because of their intrinsic mathematical importance as natural, interesting examples of non-rearrangement-invariant function spaces but also in view of their applications, which include the mathematical modeling of electrorheological fluids and image restoration.The main focus of this book is to provide a solid functional-analytic background for the study of differential operators on spaces with variable integrability. It includes some novel stability phenomena which the authors have recently discovered.At the present time, this is the only book which focuses systematically on differential operators on spaces with variable integrability. The authors present a concise, natural introduction to the basic material and steadily move toward differential operators on these spaces, leading the reader quickly to current research topics.

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Page Count

223

Publisher

World Scientific

Published Date

ISBN 10

9814596337

ISBN 13

9789814596336

Eigenvalues, Embeddings and Generalised Trigonometric Functions

By: Jan Lang,David E. Edmunds

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Eigenvalues, Embeddings and Generalised Trigonometric Functions

By: Jan Lang,David E. Edmunds

The main theme of the book is the study, from the standpoint of s-numbers, of integral operators of Hardy type and related Sobolev embeddings. In the theory of s-numbers the idea is to attach to every bounded linear map between Banach spaces a monotone decreasing sequence of non-negative numbers with a view to the classification of operators according to the way in which these numbers approach a limit: approximation numbers provide an especially important example of such numbers. The asymptotic behavior of the s-numbers of Hardy operators acting between Lebesgue spaces is determined here in a wide variety of cases. The proof methods involve the geometry of Banach spaces and generalized trigonometric functions; there are connections with the theory of the p-Laplacian.

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Page Count

232

Publisher

Springer

Published Date

ISBN 10

3642184294

ISBN 13

9783642184291

Repealing National Prohibition

By: Honorée Fanonne Jeffers,David E. Kyvig

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Repealing National Prohibition

By: Honorée Fanonne Jeffers,David E. Kyvig

A study of the political reaction against the 18th Amendment, a response that led to its reversal 14 years later by the 21st Amendment. This work uses archival evidence to examine the liquor ban and to draw attention to the bi-partisan movement led by the Association Against Prohibition Amendment.

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Page Count

310

Publisher

Kent State University Press

Published Date

ISBN 10

0873386728

ISBN 13

9780873386722

Cardiac Surgery in the Adult Fifth Edition

By: Lawrence H. Cohn,David H. Adams

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Cardiac Surgery in the Adult Fifth Edition

By: Lawrence H. Cohn,David H. Adams

The most comprehensive and current full-color cardiac surgery resource – updated by leading surgeons A Doody’s Core Title for 2022! In Cardiac Surgery in the Adult, Fifth Edition, the world’s foremost cardiovascular surgeons deliver thorough, up-to-date coverage of operative strategy, decision making, technique, and pre- and post-operative management for treating the adult cardiac patient. Unmatched in both scope and clinical rigor, this classic text contains 63 chapters that highlight every important topic in cardiovascular surgery. Presented in full color, Cardiac Surgery in the Adult takes readers through the optimal treatment of congenital, acquired, infectious, and traumatic diseases of the heart and great vessels. The book opens with a history of cardiac surgery and basic cardiac science, then moves into all types of cardiac surgery, providing both practicing surgeons and residents with insight into the very latest surgical protocols. Cardiac Surgery in the Adult is logically divided into ten sections: Basics (includes history, anatomy, physiology, pharmacology, computed tomography, risk assessment, simulation, and the fully integrated cardiovascular center) Perioperative/Intraoperative Care Ischemic Heart Disease Aortic Valve Disease Mitral Valve Disease Surgery of the Great Vessels Rhythm Surgery Other Cardiac Operations (including congenital heart disease, pericardial disease, and cardiac neoplasms) Transplant and Mechanical Circulatory Support The Fifth Edition has been updated throughout, and includes the latest advances in minimally invasive surgery and simulation.

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Page Count

1454

Publisher

McGraw Hill Professional

Published Date

ISBN 10

0071846026

ISBN 13

9780071846028

Book's by David Eric Edmunds

Hardy Operators, Function Spaces and Embeddings

Hardy Operators, Function Spaces and Embeddings

Spectral Theory and Differential Operators

Spectral Theory and Differential Operators

Bounded and Compact Integral Operators

Bounded and Compact Integral Operators

Representations of Linear Operators Between Banach Spaces

Representations of Linear Operators Between Banach Spaces

Differential Operators On Spaces Of Variable Integrability

Differential Operators On Spaces Of Variable Integrability

Eigenvalues, Embeddings and Generalised Trigonometric Functions

Eigenvalues, Embeddings and Generalised Trigonometric Functions

Repealing National Prohibition

Repealing National Prohibition

Cardiac Surgery in the Adult Fifth Edition

Cardiac Surgery in the Adult Fifth Edition

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