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Author : David E Edmunds,W Desmond Evans
Publisher : Springer
Page : 344 pages
File Size : 44,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662077329
Author : David E. Edmunds,William D. Evans
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 54,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662077313
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.
Author : Óscar Domínguez,Sergei Tikhonov
Publisher : American Mathematical Society
Page : 180 pages
File Size : 42,7 Mb
Release : 2023-02-13
Category : Mathematics
ISBN : 9781470455385
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Author : B. Malcolm Brown,Jan Lang,Ian G. Wood
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 48,6 Mb
Release : 2011-11-06
Category : Mathematics
ISBN : 9783034802635
This is a collection of contributed papers which focus on recent results in areas of differential equations, function spaces, operator theory and interpolation theory. In particular, it covers current work on measures of non-compactness and real interpolation, sharp Hardy-Littlewood-Sobolev inequalites, the HELP inequality, error estimates and spectral theory of elliptic operators, pseudo differential operators with discontinuous symbols, variable exponent spaces and entropy numbers. These papers contribute to areas of analysis which have been and continue to be heavily influenced by the leading British analysts David Edmunds and Des Evans. This book marks their respective 80th and 70th birthdays.
Author : Pankaj Jain,Hans-Jürgen Schmeisser
Publisher : Springer
Page : 335 pages
File Size : 44,6 Mb
Release : 2017-10-20
Category : Mathematics
ISBN : 9789811061196
This book features original research and survey articles on the topics of function spaces and inequalities. It focuses on (variable/grand/small) Lebesgue spaces, Orlicz spaces, Lorentz spaces, and Morrey spaces and deals with mapping properties of operators, (weighted) inequalities, pointwise multipliers and interpolation. Moreover, it considers Sobolev–Besov and Triebel–Lizorkin type smoothness spaces. The book includes papers by leading international researchers, presented at the International Conference on Function Spaces and Inequalities, held at the South Asian University, New Delhi, India, on 11–15 December 2015, which focused on recent developments in the theory of spaces with variable exponents. It also offers further investigations concerning Sobolev-type embeddings, discrete inequalities and harmonic analysis. Each chapter is dedicated to a specific topic and written by leading experts, providing an overview of the subject and stimulating future research.
Author : Alexander A. Balinsky,W. Desmond Evans,Roger T. Lewis
Publisher : Springer
Page : 263 pages
File Size : 48,9 Mb
Release : 2015-10-20
Category : Mathematics
ISBN : 9783319228709
This volume presents advances that have been made over recent decades in areas of research featuring Hardy's inequality and related topics. The inequality and its extensions and refinements are not only of intrinsic interest but are indispensable tools in many areas of mathematics and mathematical physics. Hardy inequalities on domains have a substantial role and this necessitates a detailed investigation of significant geometric properties of a domain and its boundary. Other topics covered in this volume are Hardy- Sobolev-Maz’ya inequalities; inequalities of Hardy-type involving magnetic fields; Hardy, Sobolev and Cwikel-Lieb-Rosenbljum inequalities for Pauli operators; the Rellich inequality. The Analysis and Geometry of Hardy’s Inequality provides an up-to-date account of research in areas of contemporary interest and would be suitable for a graduate course in mathematics or physics. A good basic knowledge of real and complex analysis is a prerequisite.
Author : D. E. Edmunds,W.D. Evans
Publisher : Springer
Page : 322 pages
File Size : 53,9 Mb
Release : 2018-11-20
Category : Mathematics
ISBN : 9783030021252
This book deals with elliptic differential equations, providing the analytic background necessary for the treatment of associated spectral questions, and covering important topics previously scattered throughout the literature. Starting with the basics of elliptic operators and their naturally associated function spaces, the authors then proceed to cover various related topics of current and continuing importance. Particular attention is given to the characterisation of self-adjoint extensions of symmetric operators acting in a Hilbert space and, for elliptic operators, the realisation of such extensions in terms of boundary conditions. A good deal of material not previously available in book form, such as the treatment of the Schauder estimates, is included. Requiring only basic knowledge of measure theory and functional analysis, the book is accessible to graduate students and will be of interest to all researchers in partial differential equations. The reader will value its self-contained, thorough and unified presentation of the modern theory of elliptic operators.
Author : Ben-Zion A. Rubshtein,Genady Ya. Grabarnik,Mustafa A. Muratov,Yulia S. Pashkova
Publisher : Springer
Page : 262 pages
File Size : 49,7 Mb
Release : 2016-12-09
Category : Mathematics
ISBN : 9783319427584
Key definitions and results in symmetric spaces, particularly Lp, Lorentz, Marcinkiewicz and Orlicz spaces are emphasized in this textbook. A comprehensive overview of the Lorentz, Marcinkiewicz and Orlicz spaces is presented based on concepts and results of symmetric spaces. Scientists and researchers will find the application of linear operators, ergodic theory, harmonic analysis and mathematical physics noteworthy and useful. This book is intended for graduate students and researchers in mathematics and may be used as a general reference for the theory of functions, measure theory, and functional analysis. This self-contained text is presented in four parts totaling seventeen chapters to correspond with a one-semester lecture course. Each of the four parts begins with an overview and is subsequently divided into chapters, each of which concludes with exercises and notes. A chapter called “Complements” is included at the end of the text as supplementary material to assist students with independent work.
Author : Constantine Georgakis,Alexander M. Stokolos,Wilfredo Urbina
Publisher : Springer
Page : 248 pages
File Size : 44,8 Mb
Release : 2014-11-07
Category : Mathematics
ISBN : 9783319105451
This volume of papers presented at the conference in honor of Calixto P. Calderón by his friends, colleagues, and students is intended to make the mathematical community aware of his important scholarly and research contributions in contemporary Harmonic Analysis and Mathematical Models applied to Biology and Medicine, and to stimulate further research in the future in this area of pure and applied mathematics.
Author : Dorina Mitrea,Marius Mitrea
Publisher : American Mathematical Soc.
Page : 446 pages
File Size : 42,9 Mb
Release : 2008
Category : Differential equations, Partial
ISBN : 9780821844243
This volume contains a collection of papers contributed on the occasion of Mazya's 70th birthday by a distinguished group of experts of international stature in the fields of harmonic analysis, partial differential equations, function theory, and spectral analysis, reflecting the state of the art in these areas.
Author : Nicola Arcozzi,Richard Rochberg,Eric T. Sawyer,Brett D. Wick
Publisher : American Mathematical Soc.
Page : 536 pages
File Size : 54,7 Mb
Release : 2019-09-03
Category : Dirichlet principle
ISBN : 9781470450823
The study of the classical Dirichlet space is one of the central topics on the intersection of the theory of holomorphic functions and functional analysis. It was introduced about100 years ago and continues to be an area of active current research. The theory is related to such important themes as multipliers, reproducing kernels, and Besov spaces, among others. The authors present the theory of the Dirichlet space and related spaces starting with classical results and including some quite recent achievements like Dirichlet-type spaces of functions in several complex variables and the corona problem. The first part of this book is an introduction to the function theory and operator theory of the classical Dirichlet space, a space of holomorphic functions on the unit disk defined by a smoothness criterion. The Dirichlet space is also a Hilbert space with a reproducing kernel, and is the model for the dyadic Dirichlet space, a sequence space defined on the dyadic tree. These various viewpoints are used to study a range of topics including the Pick property, multipliers, Carleson measures, boundary values, zero sets, interpolating sequences, the local Dirichlet integral, shift invariant subspaces, and Hankel forms. Recurring themes include analogies, sometimes weak and sometimes strong, with the classical Hardy space; and the analogy with the dyadic Dirichlet space. The final chapters of the book focus on Besov spaces of holomorphic functions on the complex unit ball, a class of Banach spaces generalizing the Dirichlet space. Additional techniques are developed to work with the nonisotropic complex geometry, including a useful invariant definition of local oscillation and a sophisticated variation on the dyadic Dirichlet space. Descriptions are obtained of multipliers, Carleson measures, interpolating sequences, and multiplier interpolating sequences; estimates are obtained to prove corona theorems.
Author : Ari Laptev
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 44,5 Mb
Release : 2009-11-25
Category : Mathematics
ISBN : 9781441913456
This volume reflects the variety of areas where Maz'ya's results are fundamental, influential and/or pioneering. New advantages in such areas are presented by world-recognized experts and include, in particularly, Beurling's minimum principle, inverse hyperbolic problems, degenerate oblique derivative problems, the Lp-contractivity of the generated semigroups, some class of singular integral operators, general Cwikel-Lieb-Rozenblum and Lieb-Thirring inequalities,domains with rough boundaries, integral and supremum operators, finite rank Toeplitz operators, etc.
Author : Jan Lang,David Edmunds
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 55,5 Mb
Release : 2011-03-23
Category : Education
ISBN : 9783642182679
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.
Author : D. E. Edmunds,W. D. Evans
Publisher : Cambridge University Press
Page : 169 pages
File Size : 45,6 Mb
Release : 2022-10-31
Category : Mathematics
ISBN : 9781009254632
Provides an account of fractional Sobolev spaces emphasising applications to famous inequalities. Ideal for graduates and researchers.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 52,7 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9789814479264
