Download or read book Envelopes and Sharp Embeddings of Function Spaces written by Dorothee D. Haroske and published by CRC Press. This book was released on 2006-09-22 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Until now, no book has systematically presented the recently developed concept of envelopes in function spaces. Envelopes are relatively simple tools for the study of classical and more complicated spaces, such as Besov and Triebel-Lizorkin types, in limiting situations. This theory originates from the classical result of the Sobolev embedding theo

Download or read book Envelopes and Sharp Embeddings of Function Spaces written by Fred Poplin and published by Createspace Independent Publishing Platform. This book was released on 2012-03-21 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The novel is well organized into two parts, first offering a wide release and then analyzing more advanced subjects. Some of the traditional operate areas mentioned in the first aspect include Lebesgue, Lorentz, Lipschitz, and Sobolev. The writer describes growth and a continual covers and investigates their qualities. In Part II, the guide examines the outcomes for operate areas of Besov and Triebel-Lizorkin types. The writer then provides several applying the outcomes, such as Hardy-type inequalities, asymptotic reports for entropy, and approximation numbers of lightweight embeddings. As one of the key scientists in this advancing field, the writer offers a consistent demonstration of the recent improvements in operate areas, offering valuable information for learners and scientists in efficient research.

Download or read book Envelopes and Sharp Embeddings of Function Spaces written by Andy Goodwin and published by Createspace Independent Publishing Platform. This book was released on 2017-05-03 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-contained and accessible, Envelopes and Sharp Embeddings of Function Spaces provides the first detailed account of the new theory of growth and continuity envelopes in function spaces. The book is well structured into two parts, first providing a comprehensive introduction and then examining more advanced topics. Some of the classical function spaces discussed in the first part include Lebesgue, Lorentz, Lipschitz, and Sobolev. The author defines growth and continuity envelopes and examines their properties. In Part II, the book explores the results for function spaces of Besov and Triebel-Lizorkin types. The author then presents several applications of the results, including Hardy-type inequalities, asymptotic estimates for entropy, and approximation numbers of compact embeddings.

Download or read book Limiting Embeddings Entropy Numbers and Envelopes in Function Spaces written by Dorothee Haroske and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bases in Function Spaces Sampling Discrepancy Numerical Integration written by Hans Triebel and published by European Mathematical Society. This book was released on 2010 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first chapters of this book deal with Haar bases, Faber bases and some spline bases for function spaces in Euclidean $n$-space and $n$-cubes. These are used in the subsequent chapters to study sampling and numerical integration preferably in spaces with dominating mixed smoothness. The subject of the last chapter is the symbiotic relationship between numerical integration and discrepancy, measuring the deviation of sets of points from uniformity. This book is addressed to graduate students and mathematicians who have a working knowledge of basic elements of function spaces and approximation theory and who are interested in the subtle interplay between function spaces, complexity theory and number theory (discrepancy).

Download or read book Function Spaces of Logarithmic Smoothness Embeddings and Characterizations written by Óscar Domínguez and published by American Mathematical Society. This book was released on 2023-02-13 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Download or read book Theory of Function Spaces IV written by Hans Triebel and published by Springer Nature. This book was released on 2020-01-23 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the continuation of the "Theory of Function Spaces" trilogy, published by the same author in this series and now part of classic literature in the area of function spaces. It can be regarded as a supplement to these volumes and as an accompanying book to the textbook by D.D. Haroske and the author "Distributions, Sobolev spaces, elliptic equations".

Download or read book Function Spaces and Wavelets on Domains written by Hans Triebel and published by European Mathematical Society. This book was released on 2008 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelets have emerged as an important tool in analyzing functions containing discontinuities and sharp spikes. They were developed independently in the fields of mathematics, quantum physics, electrical engineering, and seismic geology. Interchanges between these fields during the last ten years have led to many new wavelet applications such as image compression, turbulence, human vision, radar, earthquake prediction, and pure mathematics applications such as solving partial differential equations. This book develops a theory of wavelet bases and wavelet frames for function spaces on various types of domains. Starting with the usual spaces on Euclidean spaces and their periodic counterparts, the exposition moves on to so-called thick domains (including Lipschitz domains and snowflake domains). Specifically, wavelet expansions and extensions to corresponding spaces on Euclidean $n$-spaces are developed. Finally, spaces on smooth and cellular domains and related manifolds are treated. Although the presentation relies on the recent theory of function spaces, basic notation and classical results are repeated in order to make the text self-contained. This book is addressed to two types of readers: researchers in the theory of function spaces who are interested in wavelets as new effective building blocks for functions and scientists who wish to use wavelet bases in classical function spaces for various applications. Adapted to the second type of reader, the preface contains a guide on where to find basic definitions and key assertions.

Download or read book Function Spaces and Inequalities written by Pankaj Jain and published by Springer. This book was released on 2017-10-20 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Limiting Embeddings Entropy Numbers and Envelopes in Function Spaces written by and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Interpolation Theory and Applications written by Michael Cwikel and published by American Mathematical Soc.. This book was released on 2007 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the Proceedings of the Conference on Interpolation Theory and Applications in honor of Professor Michael Cwikel (Miami, FL, 2006). The central topic of this book is interpolation theory in its broadest sense, with special attention to its applications to analysis. The articles include applications to classical analysis, harmonic analysis, partial differential equations, function spaces, image processing, geometry of Banach spaces, and more. This volume emphasizes remarkable connections between several branches of pure and applied analysis. Graduate students and researchers in analysis will find it very useful.

Download or read book Issues in Calculus Mathematical Analysis and Nonlinear Research 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Calculus, Mathematical Analysis, and Nonlinear Research. The editors have built Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Calculus, Mathematical Analysis, and Nonlinear Research in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Download or read book H rmander Spaces Interpolation and Elliptic Problems written by Vladimir A. Mikhailets and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-07-14 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Hörmander function spaces. This theory was constructed by the authors in a number of papers published in 2005–2009. It is distinguished by a systematic use of the method of interpolation with a functional parameter of abstract Hilbert spaces and Sobolev inner product spaces. This method, the theory and their applications are expounded for the first time in the monographic literature. The monograph is written in detail and in a reader-friendly style. The complete proofs of theorems are given. This monograph is intended for a wide range of mathematicians whose research interests concern with mathematical analysis and differential equations.

Download or read book Theory of Besov Spaces written by Yoshihiro Sawano and published by Springer. This book was released on 2018-11-04 with total page 945 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained textbook of the theory of Besov spaces and Triebel–Lizorkin spaces oriented toward applications to partial differential equations and problems of harmonic analysis. These include a priori estimates of elliptic differential equations, the T1 theorem, pseudo-differential operators, the generator of semi-group and spaces on domains, and the Kato problem. Various function spaces are introduced to overcome the shortcomings of Besov spaces and Triebel–Lizorkin spaces as well. The only prior knowledge required of readers is familiarity with integration theory and some elementary functional analysis.Illustrations are included to show the complicated way in which spaces are defined. Owing to that complexity, many definitions are required. The necessary terminology is provided at the outset, and the theory of distributions, L^p spaces, the Hardy–Littlewood maximal operator, and the singular integral operators are called upon. One of the highlights is that the proof of the Sobolev embedding theorem is extremely simple. There are two types for each function space: a homogeneous one and an inhomogeneous one. The theory of function spaces, which readers usually learn in a standard course, can be readily applied to the inhomogeneous one. However, that theory is not sufficient for a homogeneous space; it needs to be reinforced with some knowledge of the theory of distributions. This topic, however subtle, is also covered within this volume. Additionally, related function spaces—Hardy spaces, bounded mean oscillation spaces, and Hölder continuous spaces—are defined and discussed, and it is shown that they are special cases of Besov spaces and Triebel–Lizorkin spaces.

Download or read book Distributions Sobolev Spaces Elliptic Equations written by Dorothee Haroske and published by European Mathematical Society. This book was released on 2007 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is the main aim of this book to develop at an accessible, moderate level an $L_2$ theory for elliptic differential operators of second order on bounded smooth domains in Euclidean n-space, including a priori estimates for boundary-value problems in terms of (fractional) Sobolev spaces on domains and on their boundaries, together with a related spectral theory. The presentation is preceded by an introduction to the classical theory for the Laplace-Poisson equation, and some chapters provide required ingredients such as the theory of distributions, Sobolev spaces and the spectral theory in Hilbert spaces. The book grew out of two-semester courses the authors have given several times over a period of ten years at the Friedrich Schiller University of Jena. It is addressed to graduate students and mathematicians who have a working knowledge of calculus, measure theory and the basic elements of functional analysis (as usually covered by undergraduate courses) and who are seeking an accessible introduction to some aspects of the theory of function spaces and its applications to elliptic equations.

Download or read book Theory of Function Spaces III written by Hans Triebel and published by Springer Science & Business Media. This book was released on 2006-09-10 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the recent theory of function spaces, paying special attention to some recent developments related to neighboring areas such as numerics, signal processing, and fractal analysis. Local building blocks, in particular (non-smooth) atoms, quarks, wavelet bases and wavelet frames are considered in detail and applied to diverse problems, including a local smoothness theory, spaces on Lipschitz domains, and fractal analysis.

Download or read book Elliptic Differential Operators and Spectral Analysis written by D. E. Edmunds and published by Springer. This book was released on 2018-11-20 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.