Download or read book Martingale Hardy Spaces and their Applications in Fourier Analysis written by Ferenc Weisz and published by Springer. This book was released on 2006-11-15 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the theory of one- and two-parameter martingale Hardy spaces and their use in Fourier analysis, and gives a summary of the latest results in this field. A method that can be applied for both one- and two-parameter cases, the so-called atomic decomposition method, is improved and provides a new and common construction of the theory of one- and two-parameter martingale Hardy spaces. A new proof of Carleson's convergence result using martingale methods for Fourier series is given with martingale methods. The book is accessible to readers familiar with the fundamentals of probability theory and analysis. It is intended for researchers and graduate students interested in martingale theory, Fourier analysis and in the relation between them.
Download or read book Summability of Multi Dimensional Fourier Series and Hardy Spaces written by Ferenc Weisz and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The history of martingale theory goes back to the early fifties when Doob [57] pointed out the connection between martingales and analytic functions. On the basis of Burkholder's scientific achievements the mar tingale theory can perfectly well be applied in complex analysis and in the theory of classical Hardy spaces. This connection is the main point of Durrett's book [60]. The martingale theory can also be well applied in stochastics and mathematical finance. The theories of the one-parameter martingale and the classical Hardy spaces are discussed exhaustively in the literature (see Garsia [83], Neveu [138], Dellacherie and Meyer [54, 55], Long [124], Weisz [216] and Duren [59], Stein [193, 194], Stein and Weiss [192], Lu [125], Uchiyama [205]). The theory of more-parameter martingales and martingale Hardy spaces is investigated in Imkeller [107] and Weisz [216]. This is the first mono graph which considers the theory of more-parameter classical Hardy spaces. The methods of proofs for one and several parameters are en tirely different; in most cases the theorems stated for several parameters are much more difficult to verify. The so-called atomic decomposition method that can be applied both in the one-and more-parameter cases, was considered for martingales by the author in [216].
Download or read book Martingale Hardy Spaces and Summability of One Dimensional Vilenkin Fourier Series written by Lars-Erik Persson and published by Springer Nature. This book was released on 2022-11-22 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses, develops and applies the theory of Vilenkin-Fourier series connected to modern harmonic analysis. The classical theory of Fourier series deals with decomposition of a function into sinusoidal waves. Unlike these continuous waves the Vilenkin (Walsh) functions are rectangular waves. Such waves have already been used frequently in the theory of signal transmission, multiplexing, filtering, image enhancement, code theory, digital signal processing and pattern recognition. The development of the theory of Vilenkin-Fourier series has been strongly influenced by the classical theory of trigonometric series. Because of this it is inevitable to compare results of Vilenkin-Fourier series to those on trigonometric series. There are many similarities between these theories, but there exist differences also. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group. The first part of the book can be used as an introduction to the subject, and the following chapters summarize the most recent research in this fascinating area and can be read independently. Each chapter concludes with historical remarks and open questions. The book will appeal to researchers working in Fourier and more broad harmonic analysis and will inspire them for their own and their students' research. Moreover, researchers in applied fields will appreciate it as a sourcebook far beyond the traditional mathematical domains.
Download or read book Interpolation of Operators written by Colin Bennett and published by Academic Press. This book was released on 1988-04-01 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents interpolation theory from its classical roots beginning with Banach function spaces and equimeasurable rearrangements of functions, providing a thorough introduction to the theory of rearrangement-invariant Banach function spaces. At the same time, however, it clearly shows how the theory should be generalized in order to accommodate the more recent and powerful applications. Lebesgue, Lorentz, Zygmund, and Orlicz spaces receive detailed treatment, as do the classical interpolation theorems and their applications in harmonic analysis.The text includes a wide range of techniques and applications, and will serve as an amenable introduction and useful reference to the modern theory of interpolation of operators.
Download or read book The Hardy Space H1 with Non doubling Measures and Their Applications written by Dachun Yang and published by Springer. This book was released on 2014-01-04 with total page 665 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book offers an essential but accessible introduction to the discoveries first made in the 1990s that the doubling condition is superfluous for most results for function spaces and the boundedness of operators. It shows the methods behind these discoveries, their consequences and some of their applications. It also provides detailed and comprehensive arguments, many typical and easy-to-follow examples, and interesting unsolved problems. The theory of the Hardy space is a fundamental tool for Fourier analysis, with applications for and connections to complex analysis, partial differential equations, functional analysis and geometrical analysis. It also extends to settings where the doubling condition of the underlying measures may fail.
Download or read book Operator and Norm Inequalities and Related Topics written by Richard M. Aron and published by Springer Nature. This book was released on 2022-08-10 with total page 822 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inequalities play a central role in mathematics with various applications in other disciplines. The main goal of this contributed volume is to present several important matrix, operator, and norm inequalities in a systematic and self-contained fashion. Some powerful methods are used to provide significant mathematical inequalities in functional analysis, operator theory and numerous fields in recent decades. Some chapters are devoted to giving a series of new characterizations of operator monotone functions and some others explore inequalities connected to log-majorization, relative operator entropy, and the Ando-Hiai inequality. Several chapters are focused on Birkhoff–James orthogonality and approximate orthogonality in Banach spaces and operator algebras such as C*-algebras from historical perspectives to current development. A comprehensive account of the boundedness, compactness, and restrictions of Toeplitz operators can be found in the book. Furthermore, an overview of the Bishop-Phelps-Bollobás theorem is provided. The state-of-the-art of Hardy-Littlewood inequalities in sequence spaces is given. The chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.
Download or read book Martingales in Banach Spaces written by Gilles Pisier and published by Cambridge University Press. This book was released on 2016-06-06 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on applications of martingales to the geometry of Banach spaces, and is accessible to graduate students.
Download or read book Convergence and Summability of Fourier Transforms and Hardy Spaces written by Ferenc Weisz and published by Birkhäuser. This book was released on 2017-12-27 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces. To do so, it studies a general summability method known as theta-summation, which encompasses all the well-known summability methods, such as the Fejér, Riesz, Weierstrass, Abel, Picard, Bessel and Rogosinski summations. Following on the classic books by Bary (1964) and Zygmund (1968), this is the first book that considers strong summability introduced by current methodology. A further unique aspect is that the Lebesgue points are also studied in the theory of multi-dimensional summability. In addition to classical results, results from the past 20-30 years – normally only found in scattered research papers – are also gathered and discussed, offering readers a convenient “one-stop” source to support their work. As such, the book will be useful for researchers, graduate and postgraduate students alike.
Download or read book Theory of Martingales written by Robert Liptser and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 806 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rc:ndered the 'Et moi, "', si j'avait su comment CD revenir, je n'y serais point alle. ' human race. It has put common SCIIJC back Jules Verne where it belongs. on the topmost shelf next to tbe dusty canister 1abdled 'discarded non- The series is divergent; tberefore we may be sense'. able to do sometbing witb it Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ... '; 'One service logic has rendered com puter science ... '; 'One service category theory has rendered mathematics ... '. All arguably true_ And all statements obtainable this way form part of the raison d'etre of this series_ This series, Mathematics and Its ApplicatiOns, started in 1977. Now that over one hundred volumes have appeared it seems opportune to reexamine its scope_ At the time I wrote "Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches.
Download or read book The Minnesota Notes on Jordan Algebras and Their Applications written by Max Koecher and published by Springer Science & Business Media. This book was released on 1999-09-17 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a re-edition of Max Koecher's famous Minnesota Notes. The main objects are homogeneous, but not necessarily convex, cones. They are described in terms of Jordan algebras. The central point is a correspondence between semisimple real Jordan algebras and so-called omega-domains. This leads to a construction of half-spaces which give an essential part of all bounded symmetric domains. The theory is presented in a concise manner, with only elementary prerequisites. The editors have added notes on each chapter containing an account of the relevant developments of the theory since these notes were first written.
Download or read book Analysis of Divergence written by William Bray and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 7th International Workshop in Analysis and its Applications (IWAA) was held at the University of Maine, June 1-6, 1997 and featured approxi mately 60 mathematicians. The principal theme of the workshop shares the title of this volume and the latter is a direct outgrowth of the workshop. IWAA was founded in 1984 by Professor Caslav V. Stanojevic. The first meeting was held in the resort complex Kupuri, Yugoslavia, June 1-10, 1986, with two pilot meetings preceding. The Organization Committee to gether with the Advisory Committee (R. P. Boas, R. R. Goldberg, J. P. Kahne) set forward the format and content of future meetings. A certain number of papers were presented that later appeared individually in such journals as the Proceedings of the AMS, Bulletin of the AMS, Mathematis chen Annalen, and the Journal of Mathematical Analysis and its Applica tions. The second meeting took place June 1-10, 1987, at the same location. At the plenary session of this meeting it was decided that future meetings should have a principal theme. The theme for the third meeting (June 1- 10, 1989, Kupuri) was Karamata's Regular Variation. The principal theme for the fourth meeting (June 1-10, 1990, Kupuri) was Inner Product and Convexity Structures in Analysis, Mathematical Physics, and Economics. The fifth meeting was to have had the theme, Analysis and Foundations, organized in cooperation with Professor A. Blass (June 1-10, 1991, Kupuri).
Download or read book Dyadic Walsh Analysis from 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation in Science Volume 2 Extensions and Generalizations written by Radomir Stankovic and published by Springer. This book was released on 2015-12-29 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second volume of the two volumes book is dedicated to various extensions and generalizations of Dyadic (Walsh) analysis and related applications. Considered are dyadic derivatives on Vilenkin groups and various other Abelian and finite non-Abelian groups. Since some important results were developed in former Soviet Union and China, we provide overviews of former work in these countries. Further, we present translations of three papers that were initially published in Chinese. The presentation continues with chapters written by experts in the area presenting discussions of applications of these results in specific tasks in the area of signal processing and system theory. Efficient computing of related differential operators on contemporary hardware, including graphics processing units, is also considered, which makes the methods and techniques of dyadic analysis and generalizations computationally feasible. The volume 2 of the book ends with a chapter presenting open problems pointed out by several experts in the area.
Download or read book An Introduction to Analysis on Wiener Space written by Ali S. Üstünel and published by Springer. This book was released on 2006-11-14 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives the basis of the probabilistic functional analysis on Wiener space, developed during the last decade. The subject has progressed considerably in recent years thr- ough its links with QFT and the impact of Stochastic Calcu- lus of Variations of P. Malliavin. Although the latter deals essentially with the regularity of the laws of random varia- bles defined on the Wiener space, the book focuses on quite different subjects, i.e. independence, Ramer's theorem, etc. First year graduate level in functional analysis and theory of stochastic processes is required (stochastic integration with respect to Brownian motion, Ito formula etc). It can be taught as a 1-semester course as it is, or in 2 semesters adding preliminaries from the theory of stochastic processes It is a user-friendly introduction to Malliavin calculus!
Download or read book Real Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko written by Yinqin Li and published by Springer Nature. This book was released on 2023-02-14 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: The real-variable theory of function spaces has always been at the core of harmonic analysis. In particular, the real-variable theory of the Hardy space is a fundamental tool of harmonic analysis, with applications and connections to complex analysis, partial differential equations, and functional analysis. This book is devoted to exploring properties of generalized Herz spaces and establishing a complete real-variable theory of Hardy spaces associated with local and global generalized Herz spaces via a totally fresh perspective. This means that the authors view these generalized Herz spaces as special cases of ball quasi-Banach function spaces. In this book, the authors first give some basic properties of generalized Herz spaces and obtain the boundedness and the compactness characterizations of commutators on them. Then the authors introduce the associated Herz–Hardy spaces, localized Herz–Hardy spaces, and weak Herz–Hardy spaces, and develop a complete real-variable theory of these Herz–Hardy spaces, including their various maximal function, atomic, molecular as well as various Littlewood–Paley function characterizations. As applications, the authors establish the boundedness of some important operators arising from harmonic analysis on these Herz–Hardy spaces. Finally, the inhomogeneous Herz–Hardy spaces and their complete real-variable theory are also investigated. With the fresh perspective and the improved conclusions on the real-variable theory of Hardy spaces associated with ball quasi-Banach function spaces, all the obtained results of this book are new and their related exponents are sharp. This book will be appealing to researchers and graduate students who are interested in function spaces and their applications.
Download or read book Classical Fourier Analysis written by Loukas Grafakos and published by Springer Science & Business Media. This book was released on 2008-09-18 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. This book is mainly addressed to graduate students in mathematics and is designed to serve for a three-course sequence on the subject. The only prerequisite for understanding the text is satisfactory completion of a course in measure theory, Lebesgue integration, and complex variables. This book is intended to present the selected topics in some depth and stimulate further study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of analysis on the torus. This material is included for historical reasons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in several variables. While the 1st edition was published as a single volume, the new edition will contain 120 pp of new material, with an additional chapter on time-frequency analysis and other modern topics. As a result, the book is now being published in 2 separate volumes, the first volume containing the classical topics (Lp Spaces, Littlewood-Paley Theory, Smoothness, etc...), the second volume containing the modern topics (weighted inequalities, wavelets, atomic decomposition, etc...). From a review of the first edition: “Grafakos’s book is very user-friendly with numerous examples illustrating the definitions and ideas. It is more suitable for readers who want to get a feel for current research. The treatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises.” - Ken Ross, MAA Online
Download or read book Generalized Heisenberg Groups and Damek Ricci Harmonic Spaces written by Jürgen Berndt and published by Springer. This book was released on 2006-11-14 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Heisenberg groups, or H-type groups, introduced by A. Kaplan, and Damek-Ricci harmonic spaces are particularly nice Lie groups with a vast spectrum of properties and applications. These harmonic spaces are homogeneous Hadamard manifolds containing the H-type groups as horospheres. These notes contain a thorough study of their Riemannian geometry by means of a detailed treatment of their Jacobi vector fields and Jacobi operators. Some problems are included and will hopefully stimulate further research on these spaces. The book is written for students and researchers, assuming only basic knowledge of Riemannian geometry, and it contains a brief survey of the background material needed to follow the entire treatment.
Download or read book Topics in the Theory of Riemann Surfaces written by Robert D.M. Accola and published by Springer. This book was released on 2006-11-14 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book's main concern is automorphisms of Riemann surfaces, giving a foundational treatment from the point of view of Galois coverings, and treating the problem of the largest automorphism group for a Riemann surface of a given genus. In addition, the extent to which fixed points of automorphisms are generalized Weierstrass points is considered. The extremely useful inequality of Castelnuovo- Severi is also treated. While the methods are elementary, much of the material does not appear in the current texts on Riemann surfaces, algebraic curves. The book is accessible to a reader who has had an introductory course on the theory of Riemann surfaces or algebraic curves.
