Locally Convex Spaces And Harmonic Analysis An Introduction
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| Author | : Philippe G. Ciarlet |
| Publisher | : SIAM |
| Total Pages | : 203 |
| Release | : 2021-08-10 |
| Genre | : Mathematics |
| ISBN | : 1611976650 |
This self-contained textbook covers the fundamentals of two basic topics of linear functional analysis: locally convex spaces and harmonic analysis. Readers will find detailed introductions to topological vector spaces, distribution theory, weak topologies, the Fourier transform, the Hilbert transform, and Calderón–Zygmund singular integrals. An ideal introduction to more advanced texts, the book complements Ciarlet’s Linear and Nonlinear Functional Analysis with Applications (SIAM), in which these two topics were not treated. Pedagogical features such as detailed proofs and 93 problems make the book ideal for a one-semester first-year graduate course or for self-study. The book is intended for advanced undergraduates and first-year graduate students and researchers. It is appropriate for courses on functional analysis, distribution theory, Fourier transform, and harmonic analysis.
| Author | : Gerald B. Folland |
| Publisher | : CRC Press |
| Total Pages | : 317 |
| Release | : 2016-02-03 |
| Genre | : Mathematics |
| ISBN | : 1498727158 |
A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant resul
| Author | : C. Perez-Garcia |
| Publisher | : Cambridge University Press |
| Total Pages | : 486 |
| Release | : 2010-01-07 |
| Genre | : Mathematics |
| ISBN | : 9780521192439 |
Non-Archimedean functional analysis, where alternative but equally valid number systems such as p-adic numbers are fundamental, is a fast-growing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry. This book is the first to provide a comprehensive treatment of non-Archimedean locally convex spaces. The authors provide a clear exposition of the basic theory, together with complete proofs and new results from the latest research. A guide to the many illustrative examples provided, end-of-chapter notes and glossary of terms all make this book easily accessible to beginners at the graduate level, as well as specialists from a variety of disciplines.
| Author | : James W. Demmel |
| Publisher | : SIAM |
| Total Pages | : 426 |
| Release | : 1997-08-01 |
| Genre | : Mathematics |
| ISBN | : 0898713897 |
This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.
| Author | : Gerrit van Dijk |
| Publisher | : Walter de Gruyter |
| Total Pages | : 234 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 3110220199 |
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
| Author | : H. Garth Dales |
| Publisher | : Cambridge University Press |
| Total Pages | : 338 |
| Release | : 2003-11-13 |
| Genre | : Mathematics |
| ISBN | : 9780521535847 |
| Author | : C. van den Berg |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 299 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 146121128X |
The Fourier transform and the Laplace transform of a positive measure share, together with its moment sequence, a positive definiteness property which under certain regularity assumptions is characteristic for such expressions. This is formulated in exact terms in the famous theorems of Bochner, Bernstein-Widder and Hamburger. All three theorems can be viewed as special cases of a general theorem about functions qJ on abelian semigroups with involution (S, +, *) which are positive definite in the sense that the matrix (qJ(sJ + Sk» is positive definite for all finite choices of elements St, . . . , Sn from S. The three basic results mentioned above correspond to (~, +, x* = -x), ([0, 00[, +, x* = x) and (No, +, n* = n). The purpose of this book is to provide a treatment of these positive definite functions on abelian semigroups with involution. In doing so we also discuss related topics such as negative definite functions, completely mono tone functions and Hoeffding-type inequalities. We view these subjects as important ingredients of harmonic analysis on semigroups. It has been our aim, simultaneously, to write a book which can serve as a textbook for an advanced graduate course, because we feel that the notion of positive definiteness is an important and basic notion which occurs in mathematics as often as the notion of a Hilbert space.
| Author | : M. Scott Osborne |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 217 |
| Release | : 2013-11-08 |
| Genre | : Mathematics |
| ISBN | : 3319020455 |
For most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research. This graduate text, while focusing on locally convex topological vector spaces, is intended to cover most of the general theory needed for application to other areas of analysis. Normed vector spaces, Banach spaces, and Hilbert spaces are all examples of classes of locally convex spaces, which is why this is an important topic in functional analysis. While this graduate text focuses on what is needed for applications, it also shows the beauty of the subject and motivates the reader with exercises of varying difficulty. Key topics covered include point set topology, topological vector spaces, the Hahn–Banach theorem, seminorms and Fréchet spaces, uniform boundedness, and dual spaces. The prerequisite for this text is the Banach space theory typically taught in a beginning graduate real analysis course.
| Author | : Camil Muscalu |
| Publisher | : Cambridge University Press |
| Total Pages | : 389 |
| Release | : 2013-01-31 |
| Genre | : Mathematics |
| ISBN | : 1139619160 |
This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón–Zygmund and Littlewood–Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman–Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form.
| Author | : Vladimir I. Bogachev |
| Publisher | : Springer Nature |
| Total Pages | : 586 |
| Release | : 2020-02-25 |
| Genre | : Mathematics |
| ISBN | : 3030382192 |
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.
