Download or read book Boundary Value Problems for Analytic and Harmonic Functions in Nonstandard Banach Function Spaces written by Vakhtang Mikhaĭlovich Kokilashvili and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the boundary value problems (BVPs) for analytic and harmonic functions in domains with non-smooth boundaries within the framework of non-standard Banach function spaces, namely, variable exponent Lebesgue spaces and grand Lebesgue spaces. This book is aimed at a wide audience, ranging from researchers in BVPs of function theory and mathematical physics to experts in theory of elasticity and post-graduate students.
Download or read book Integral Operators in Non Standard Function Spaces written by Vakhtang Kokilashvili and published by Birkhäuser. This book was released on 2016-05-11 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the result of the authors' long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them. The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book's most distinctive features is that the majority of the statements proved here are in the form of criteria. The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.
Download or read book Monogenic Functions in Spaces with Commutative Multiplication and Applications written by Sergiy A. Plaksa and published by Springer Nature. This book was released on 2023-07-18 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph develops a theory of continuous and differentiable functions, called monogenic functions, in the sense of Gateaux functions taking values in some vector spaces with commutative multiplication. The study of these monogenic functions in various commutative algebras leads to a discovery of new ways of solving boundary value problems in mathematical physics. The book consists of six parts: Part I presents some preliminary notions and introduces various concepts of differentiable mappings of vector spaces. Part II - V is devoted to the study of monogenic functions in various spaces with commutative multiplication, namely, three dimensional commutative algebras with two-dimensional radical, finite-dimensional commutative associative algebras, infinite-dimensional vector spaces associated with the three-dimensional Laplace equation and infinite-dimensional vector spaces associated with axial-symmetric potential fields. Part VI presents some boundary value problems for axial-symmetric potential fields and develops effective analytic methods of solving these boundary value problems with various applications in mathematical physics. Graduate students and researchers alike benefit from this book.
Download or read book Integral Operators in Non Standard Function Spaces written by Vakhtang Kokilashvili and published by Birkhäuser. This book was released on 2024-09-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present monograph serves as a natural extension of the prior 2-volume monograph with the same title and by the same authors, which encompassed findings up until 2014. This four-volume project encapsulates the authors’ decade-long research in the trending topic of nonstandard function spaces and operator theory. One of the main novelties of the present book is to develop the extrapolation theory, generally speaking, in grand Banach function spaces, and to apply it for obtaining the boundedness of fundamental operators of harmonic analysis, in particular, function spaces such as grand weighted Lebesgue and Lorentz spaces, grand variable exponent Lebesgue/Morrey spaces, mixed normed function spaces, etc. Embeddings in grand variable exponent Hajłasz-Sobolev spaces are also studied. Some applications to the approximation theory and boundary value problems of analytic functions are presented as well. The book is aimed at an audience ranging from researchers in operator theory and harmonic analysis to experts in applied mathematics and post graduate students. In particular, we hope that this book will serve as a source of inspiration for researchers in abstract harmonic analysis, function spaces, PDEs and boundary value problems.
Download or read book Modern Aspects of the Theory of Partial Differential Equations written by Michael Ruzhansky and published by Springer Science & Business Media. This book was released on 2011-05-04 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a quick overview of a wide range of active research areas in partial differential equations. The book can serve as a useful source of information to mathematicians, scientists and engineers. The volume contains contributions from authors from a large variety of countries on different aspects of partial differential equations, such as evolution equations and estimates for their solutions, control theory, inverse problems, nonlinear equations, elliptic theory on singular domains, numerical approaches.
Download or read book Topics in Complex Analysis and Function Spaces written by Mark Hoffmann and published by . This book was released on 2003 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are three parts of this work. In the first part we give an explicit computation of the Banach envelope for non-locally convex Paley-Wiener type spaces. In the second part we develop more general tools for the treatment of harmonic and analytic functions which take values in a quasi-Banach space. We are able to give a description of boundary value functions for the classes [Special characters omitted.] . Our results extend the well known case of scalar valued functions on the disc and the half plane. The third part is joint work with Nigel Kalton and Tamara Kucherenko. It is shown that R -bounded and weakly compact semigroups on L [subscript 1] and C (K) can only exist for [cursive l] [subscript 1] and c [subscript 0]. More generally, R -bounded weakly compact commuting approximating sequences in Banach spaces are discussed.
Download or read book Functional Analysis and Boundary value Problems written by B. Dayanand Reddy and published by Longman Scientific and Technical. This book was released on 1986 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Continual Means and Boundary Value Problems in Function Spaces written by E. M. Polishchuk and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-01-19 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Boundary Value Problems for Elliptic Equations and Systems written by Guo Chun Wen and published by Longman Scientific and Technical. This book was released on 1990 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lebesgue and Sobolev Spaces with Variable Exponents written by Lars Diening and published by Springer Science & Business Media. This book was released on 2011-03-31 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.
Download or read book Spaces of Analytic Functions written by O.B. Bekken and published by Springer. This book was released on 2006-11-14 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonstandard Methods in the Calculus of Variations written by Curtis Tuckey and published by CRC Press. This book was released on 1993-11-22 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is unique in its treatment of the application of methods of nonstandard analysis to the theory of curves in the calculus of variations. It will be of particular value to researchers in the calculus of variations and optimal control theory.
Download or read book FUNCTIONAL ANALYSIS AND BOUNDARY VALUE PROBLEMS written by Lamberto Cesari and published by . This book was released on 1970 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Continual Means and Boundary Value Problems in Function Spaces written by Efim Mikhaĭlovich Polishchuk and published by . This book was released on 1988 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Boundary Value Problems and Singular Integral Equations on Banach Function Spaces written by and published by . This book was released on 2015 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book U S Government Research Reports written by and published by . This book was released on 1962 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Generalized Functions and Their Applications written by R.S. Pathak and published by Springer. This book was released on 1993-04-30 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Symposium on Generalized Functions and Their Applications was organized by the Department of Mathematics, Banaras Hindu University, and held December 23-26, 1991, on the occasion of the Platinum Jubilee Celebration of the university. More than a hundred mathematicians from ten countries participated in the deliberations of the symposium. Thirty lectures were delivered on a variety of topics within the area. The contributions to the proceedings of the symposium are, with a few exceptions, expanded versions of the lectures delivered by the invited speakers. The survey papers by Komatsu and Hoskins and Sousa Pinto provide an up-to-date account of the theory of hyperfunctions, ultradistributions and microfunctions, and the nonstandard theory of new generalized functions, respectively; those by Stankovic and Kanwal deal with structures and asymptotics. Choquet-Bruhat's work studies generalized functions on manifold and gives applications to shocks and discrete models. The other contributions relate to contemporary problems and achievements in theory and applications, especially in the theory of partial differential equations, differential geometry, mechanics, mathematical physics, and systems science. The proceedings give a very clear impression of the present state of the art in this field and contain many challenges, ideas, and open problems. The volume is very helpful for a broad spectrum of readers: graduate students to mathematical researchers.
