Download or read book Theory of Sobolev Multipliers written by Vladimir Maz'ya and published by Springer Science & Business Media. This book was released on 2008-10-13 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this book offers a comprehensive overview of the theory of pointwise multipliers acting in pairs of spaces of differentiable functions. The second part of the book explores several applications of this theory.
Download or read book Theory of Sobolev Multipliers written by and published by . This book was released on 2009 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory of Multipliers in Spaces of Differentiable Functions written by V. G. Mazʹi︠a︡ and published by Pitman Publishing. This book was released on 1985 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory of Multipliers in Spaces of Differential Functions written by Vladimir G. Maz'ya and published by Halsted Press. This book was released on 1986-05-01 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Theory of Ultraspherical Multipliers written by William Carroll Connett and published by American Mathematical Soc.. This book was released on 1977 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many multiplier theorems of Fourier analysis have analogs for ultraspherical expansions. But what was a single theorem in the Fourier setting becomes an entire family of theorems in this more general setting. The problem solved in this paper is that of organizing the children of the Fourier theorems, and many new theorems besides, into a coherent theory. The most critical step in this organization is identifying a family of Banach spaces which include the sequences described in the classical multiplier theorems as special cases. Once this family is found, the next step is to develop the methods of interpolation necessary to show that this family forms a scale of spaces--in the sense that if two spaces in the family act as multipliers on L[superscript]p, then all spaces "between" these two spaces act as multipliers on L[superscript]p.
Download or read book Harmonic Analysis and Partial Differential Equations written by Anatoly Golberg and published by Springer Nature. This book was released on 2023-04-26 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Vladimir Maz'ya has made a number of groundbreaking contributions to numerous areas of mathematics, including partial differential equations, function theory, and harmonic analysis. The chapters in this volume - compiled on the occasion of his 80th birthday - are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.
Download or read book Beyond Sobolev and Besov written by Cornelia Schneider and published by Springer Nature. This book was released on 2021-05-31 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates the close relation between quite sophisticated function spaces, the regularity of solutions of partial differential equations (PDEs) in these spaces and the link with the numerical solution of such PDEs. It consists of three parts. Part I, the introduction, provides a quick guide to function spaces and the general concepts needed. Part II is the heart of the monograph and deals with the regularity of solutions in Besov and fractional Sobolev spaces. In particular, it studies regularity estimates of PDEs of elliptic, parabolic and hyperbolic type on non smooth domains. Linear as well as nonlinear equations are considered and special attention is paid to PDEs of parabolic type. For the classes of PDEs investigated a justification is given for the use of adaptive numerical schemes. Finally, the last part has a slightly different focus and is concerned with traces in several function spaces such as Besov– and Triebel–Lizorkin spaces, but also in quite general smoothness Morrey spaces. The book is aimed at researchers and graduate students working in regularity theory of PDEs and function spaces, who are looking for a comprehensive treatment of the above listed topics.
Download or read book Sobolev Spaces written by Vladimir Maz'ya and published by Springer Science & Business Media. This book was released on 2011-02-11 with total page 882 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable tool in approximation theory, spectral theory, differential geometry etc. The theory of these spaces is of interest in itself being a beautiful domain of mathematics. The present volume includes basics on Sobolev spaces, approximation and extension theorems, embedding and compactness theorems, their relations with isoperimetric and isocapacitary inequalities, capacities with applications to spectral theory of elliptic differential operators as well as pointwise inequalities for derivatives. The selection of topics is mainly influenced by the author’s involvement in their study, a considerable part of the text is a report on his work in the field. Part of this volume first appeared in German as three booklets of Teubner-Texte zur Mathematik (1979, 1980). In the Springer volume “Sobolev Spaces”, published in English in 1985, the material was expanded and revised. The present 2nd edition is enhanced by many recent results and it includes new applications to linear and nonlinear partial differential equations. New historical comments, five new chapters and a significantly augmented list of references aim to create a broader and modern view of the area.
Download or read book Elliptic Equations in Polyhedral Domains written by V. G. Maz_i_a and published by American Mathematical Soc.. This book was released on 2010-04-22 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph which systematically treats elliptic boundary value problems in domains of polyhedral type. The authors mainly describe their own recent results focusing on the Dirichlet problem for linear strongly elliptic systems of arbitrary order, Neumann and mixed boundary value problems for second order systems, and on boundary value problems for the stationary Stokes and Navier-Stokes systems. A feature of the book is the systematic use of Green's matrices. Using estimates for the elements of these matrices, the authors obtain solvability and regularity theorems for the solutions in weighted and non-weighted Sobolev and Holder spaces. Some classical problems of mathematical physics (Laplace and biharmonic equations, Lame system) are considered as examples. Furthermore, the book contains maximum modulus estimates for the solutions and their derivatives. The exposition is self-contained, and an introductory chapter provides background material on the theory of elliptic boundary value problems in domains with smooth boundaries and in domains with conical points. The book is destined for graduate students and researchers working in elliptic partial differential equations and applications.
Download or read book The Maz ya Anniversary Collection written by Jürgen Rossmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions in this volume are dedicated to Vladimir G. Maz'ya and are par tially based on talks given at the conference "Functional Analysis, Partial Differ ential Equations, and Applications", which took place at the University of Rostock from August 31 to September 4, 1998, to honour Prof. Maz'ya. This conference (a satellite meeting of the ICM) gave an opportunity to many friends and colleagues from all over the world to honour him. This academic community is very large. The scientific field of Prof. Maz'ya is impressively broad, which is reflected in the variety of contributions included in the volumes. Vladimir Maz'ya is the author and co-author of many publications (see the list of publications at the end of this volume), the topics of which extend from functional analysis, function theory and numerical analysis to partial differential equations and their broad applications. Vladimir G. Maz'ya provided significant contributions, among others to the the ory of Sobolev spaces, the capacity theory, boundary integral methods, qualitative and asymptotic methods of analysis of linear and nonlinear elliptic differential equations, the Cauchy problem for elliptic and hyperbolic equations, the theory of multipliers in spaces of differentiable functions, maximum principles for elliptic and parabolic systems, and boundary value problems in domains with piecewise smooth boundaries. Surveys on Maz'ya's work in different fields of mathematics and areas, where he made essential contributions, form a major part of the present first volume of The Maz'ya Anniversary Collection.
Download or read book Morrey Spaces written by David Adams and published by Birkhäuser. This book was released on 2015-12-31 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this set of lecture notes, the author includes some of the latest research on the theory of Morrey Spaces associated with Harmonic Analysis. There are three main claims concerning these spaces that are covered: determining the integrability classes of the trace of Riesz potentials of an arbitrary Morrey function; determining the dimensions of singular sets of weak solutions of PDE (e.g. The Meyers-Elcart System); and determining whether there are any “full” interpolation results for linear operators between Morrey spaces. This book will serve as a useful reference to graduate students and researchers interested in Potential Theory, Harmonic Analysis, PDE, and/or Morrey Space Theory.
Download or read book Analysis Partial Differential Equations and Applications written by Alberto Cialdea and published by Springer Science & Business Media. This book was released on 2010-01-14 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes several invited lectures given at the International Workshop "Analysis, Partial Differential Equations and Applications", held at the Mathematical Department of Sapienza University of Rome, on the occasion of the 70th birthday of Vladimir G. Maz'ya, a renowned mathematician and one of the main experts in the field of pure and applied analysis. The book aims at spreading the seminal ideas of Maz'ya to a larger audience in faculties of sciences and engineering. In fact, all articles were inspired by previous works of Maz'ya in several frameworks, including classical and contemporary problems connected with boundary and initial value problems for elliptic, hyperbolic and parabolic operators, Schrödinger-type equations, mathematical theory of elasticity, potential theory, capacity, singular integral operators, p-Laplacians, functional analysis, and approximation theory. Maz'ya is author of more than 450 papers and 20 books. In his long career he obtained many astonishing and frequently cited results in the theory of harmonic potentials on non-smooth domains, potential and capacity theories, spaces of functions with bounded variation, maximum principle for higher-order elliptic equations, Sobolev multipliers, approximate approximations, etc. The topics included in this volume will be particularly useful to all researchers who are interested in achieving a deeper understanding of the large expertise of Vladimir Maz'ya.
Download or read book Singular Integrals and Fourier Theory on Lipschitz Boundaries written by Tao Qian and published by Springer. This book was released on 2019-03-20 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book is to provide a detailed and comprehensive survey of the theory of singular integrals and Fourier multipliers on Lipschitz curves and surfaces, an area that has been developed since the 1980s. The subject of singular integrals and the related Fourier multipliers on Lipschitz curves and surfaces has an extensive background in harmonic analysis and partial differential equations. The book elaborates on the basic framework, the Fourier methodology, and the main results in various contexts, especially addressing the following topics: singular integral operators with holomorphic kernels, fractional integral and differential operators with holomorphic kernels, holomorphic and monogenic Fourier multipliers, and Cauchy-Dunford functional calculi of the Dirac operators on Lipschitz curves and surfaces, and the high-dimensional Fueter mapping theorem with applications. The book offers a valuable resource for all graduate students and researchers interested in singular integrals and Fourier multipliers.
Download or read book Decay of the Fourier Transform written by Alex Iosevich and published by Springer. This book was released on 2014-10-01 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Plancherel formula says that the L^2 norm of the function is equal to the L^2 norm of its Fourier transform. This implies that at least on average, the Fourier transform of an L^2 function decays at infinity. This book is dedicated to the study of the rate of this decay under various assumptions and circumstances, far beyond the original L^2 setting. Analytic and geometric properties of the underlying functions interact in a seamless symbiosis which underlines the wide range influences and applications of the concepts under consideration.
Download or read book Morrey Spaces written by Yoshihiro Sawano and published by CRC Press. This book was released on 2020-09-16 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume II focused mainly generalizations and interpolation of Morrey spaces. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding
Download or read book Real and Functional Analysis written by Vladimir I. Bogachev and published by Springer Nature. This book was released on 2020-02-25 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.
Download or read book Function Spaces and Partial Differential Equations written by Ali Taheri and published by Oxford University Press. This book was released on 2015-07-30 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.
