Functions of Generalized Bounded Variation, Generalized Absolute Continuity and Applications to Fourier Series
Author: Nunzio Paul Schembari
Publisher:
Published: 1991
Total Pages: 78
ISBN-13:
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Author: Nunzio Paul Schembari
Publisher:
Published: 1991
Total Pages: 78
ISBN-13:
DOWNLOAD EBOOKAuthor: Jürgen Appell
Publisher: Walter de Gruyter
Published: 2013-12-12
Total Pages: 488
ISBN-13: 3110265117
DOWNLOAD EBOOKThe aim of this monograph is to give a thorough and self-contained account of functions of (generalized) bounded variation, the methods connected with their study, their relations to other important function classes, and their applications to various problems arising in Fourier analysis and nonlinear analysis. In the first part the basic facts about spaces of functions of bounded variation and related spaces are collected, the main ideas which are useful in studying their properties are presented, and a comparison of their importance and suitability for applications is provided, with a particular emphasis on illustrative examples and counterexamples. The second part is concerned with (sometimes quite surprising) properties of nonlinear composition and superposition operators in such spaces. Moreover, relations with Riemann-Stieltjes integrals, convergence tests for Fourier series, and applications to nonlinear integral equations are discussed. The only prerequisite for understanding this book is a modest background in real analysis, functional analysis, and operator theory. It is addressed to non-specialists who want to get an idea of the development of the theory and its applications in the last decades, as well as a glimpse of the diversity of the directions in which current research is moving. Since the authors try to take into account recent results and state several open problems, this book might also be a fruitful source of inspiration for further research.
Author: Elijah Liflyand
Publisher: Springer
Published: 2019-03-06
Total Pages: 194
ISBN-13: 3030044297
DOWNLOAD EBOOKFunctions of bounded variation represent an important class of functions. Studying their Fourier transforms is a valuable means of revealing their analytic properties. Moreover, it brings to light new interrelations between these functions and the real Hardy space and, correspondingly, between the Fourier transform and the Hilbert transform. This book is divided into two major parts, the first of which addresses several aspects of the behavior of the Fourier transform of a function of bounded variation in dimension one. In turn, the second part examines the Fourier transforms of multivariate functions with bounded Hardy variation. The results obtained are subsequently applicable to problems in approximation theory, summability of the Fourier series and integrability of trigonometric series.
Author: John L. Challifour
Publisher:
Published: 1972
Total Pages: 208
ISBN-13:
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Publisher:
Published: 1989
Total Pages: 16
ISBN-13:
DOWNLOAD EBOOKAuthor: Robert E. Edwards
Publisher:
Published: 1979
Total Pages: 242
ISBN-13:
DOWNLOAD EBOOKAuthor: Laura De Carli
Publisher: World Scientific
Published: 2008-10-08
Total Pages: 202
ISBN-13: 9814469998
DOWNLOAD EBOOKThis book covers a wide range of topics, from orthogonal polynomials to wavelets. It contains several high-quality research papers by prominent experts exploring trends in function theory, orthogonal polynomials, Fourier series, approximation theory, theory of wavelets and applications. The book provides an up-to-date presentation of several important topics in Classical and Modern Analysis. The interested reader will also be able to find stimulating open problems and suggestions for future research.
Author: Michael Oberguggenberger
Publisher: Birkhäuser
Published: 2017-05-06
Total Pages: 280
ISBN-13: 3319519115
DOWNLOAD EBOOKThis book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis. The volume is a collection of chapters addressing these fields, their interaction, their unifying concepts and their applications and is based on scientific activities related to the International Association for Generalized Functions (IAGF) and the ISAAC interest groups on Pseudo-Differential Operators (IGPDO) and on Generalized Functions (IGGF), notably on the longstanding collaboration of these groups within ISAAC.
Author: Horatio Scott Carslaw
Publisher:
Published: 1930
Total Pages: 394
ISBN-13:
DOWNLOAD EBOOKAuthor: Sir M. J. Lighthill
Publisher: Cambridge University Press
Published: 1958
Total Pages: 112
ISBN-13: 9780521091282
DOWNLOAD EBOOK"Clearly and attractively written, but without any deviation from rigorous standards of mathematical proof...." Science Progress