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Fourier Transforms And Spectral Synthesis On Locally Compact Abelian Groups
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Book Synopsis Aspects Of Harmonic Analysis On Locally Compact Abelian Groups by : Jean H Gallier
Download or read book Aspects Of Harmonic Analysis On Locally Compact Abelian Groups written by Jean H Gallier and published by World Scientific. This book was released on 2024-06-21 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fourier transform is a 'tool' used in engineering and computer vision to model periodic phenomena. Starting with the basics of measure theory and integration, this book delves into the harmonic analysis of locally compact abelian groups. It provides an in-depth tour of the beautiful theory of the Fourier transform based on the results of Gelfand, Pontrjagin, and Andre Weil in a manner accessible to an undergraduate student who has taken linear algebra and introductory real analysis.Highlights of this book include the Bochner integral, the Haar measure, Radon functionals, the theory of Fourier analysis on the circle, and the theory of the discrete Fourier transform. After studying this book, the reader will have the preparation necessary for understanding the Peter-Weyl theorems for complete, separable Hilbert algebras, a key theoretical concept used in the construction of Gelfand pairs and equivariant convolutional neural networks.
Book Synopsis Discrete Spectral Synthesis and Its Applications by : László Székelyhidi
Download or read book Discrete Spectral Synthesis and Its Applications written by László Székelyhidi and published by Springer Science & Business Media. This book was released on 2007-01-25 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the situation over discrete Abelian groups with wide range applications. It covers classical functional equations, difference and differential equations, polynomial ideals, digital filtering and polynomial hypergroups, giving unified treatment of several different problems. There is no other comprehensive work in this field. The book will be of interest to graduate students, research workers in harmonic analysis, spectral analysis, functional equations and hypergroups.
Download or read book Spectral Synthesis written by and published by Academic Press. This book was released on 1976-06-28 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral Synthesis
Book Synopsis Harmonic Analysis by : Pierre Eymard
Download or read book Harmonic Analysis written by Pierre Eymard and published by Springer. This book was released on 2006-11-14 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Harmonic And Spectral Analysis by : Laszlo Szekelyhidi
Download or read book Harmonic And Spectral Analysis written by Laszlo Szekelyhidi and published by World Scientific. This book was released on 2014-03-19 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a modern introduction to harmonic analysis and synthesis on topological groups. It serves as a guide to the abstract theory of Fourier transformation. For the first time, it presents a detailed account of the theory of classical harmonic analysis together with the recent developments in spectral analysis and synthesis.
Book Synopsis Convolution Type Functional Equations on Topological Abelian Groups by : L szl¢ Szkelyhidi
Download or read book Convolution Type Functional Equations on Topological Abelian Groups written by L szl¢ Szkelyhidi and published by World Scientific. This book was released on 1991 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the possible applications of spectral analysis and spectral synthesis for convolution type functional equations on topological abelian groups. The solution space of convolution type equations has been synthesized in the sense that the general solutions are built up from exponential monomial solutions. In particular, equivalence of systems of functional equations can be tested. This leads to a unified treatment of classical equations and to interesting new results.
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Book Synopsis Harmonic Analysis and Number Theory by : Carl Herz
Download or read book Harmonic Analysis and Number Theory written by Carl Herz and published by American Mathematical Soc.. This book was released on 1997 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of a conference on Harmonic Analysis and Number Theory held at McGill University (Montreal) in April 1996. The papers are dedicated to the memory of Carl Herz, who had deep interests in both harmonic analysis and number theory. These two disciplines have a symbiotic relationship that is reflected in the papers in this book.
Book Synopsis Symposia on Theoretical Physics and Mathematics 9 by : Alladi Ramakrishnan
Download or read book Symposia on Theoretical Physics and Mathematics 9 written by Alladi Ramakrishnan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume represents the proceedings of the Sixth Anniversary MATSCIENCE Symposium on Theoretical Physics held in January 1968 as well as the Seminar in Analysis held earlier, in December 1967. A new feature of this volume is that it includes also contributions dealing with applications of mathematics to domains other than theoretical physics. Accordingly, the volume is divided into three parts-Part I deals with theoretical physics, Part II with applications of mathematical methods, and Part III with pure mathematics. The volume begins with a contribution from Okubo who proposed a new scheme to explain the CP puzzle by invoking the intermediate vector bosons. Gordon Shaw from Irvine dealt with the crucial importance of the effects of CDD poles in partial wave dispersion relations in dynamical calculation of resonances. Applications of current algebra and quark models were considered in the papers of Divakaran, Ramachandran, and Rajasekharan. Dubin presented a rigorous formulation of the Heisenberg ferromagnet.
Book Synopsis The Way I Remember It by : Walter Rudin
Download or read book The Way I Remember It written by Walter Rudin and published by American Mathematical Soc.. This book was released on 1997 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Walter Rudin's memoirs should prove to be a delightful read specifically to mathematicians, but also to historians who are interested in learning abou his colourful history and ancestry. Characterized by his personal style of elegance, clarity, and brevity, Rudin presents in the first part of the book his early memories about his family history, his boyhood in Vienna throughout the 1920s and 1930s, and his experiences during World War II. Part II offers samples of his work, in which he relates where problems came from, what their solutions led to, and who else was involved. As those who are familiar with Rudin's writing will recognize, he brings to this book the same care, depth, and originality that is the hallmark of his work. Co-published with the London Mathematical Society
Download or read book Honam Mathematical Journal written by and published by . This book was released on 1991 with total page 804 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Abstract Harmonic Analysis by : Edwin Hewitt
Download or read book Abstract Harmonic Analysis written by Edwin Hewitt and published by Springer. This book was released on 2013-11-11 with total page 781 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a continuation of Volume I of the same title [Grund lehren der mathematischen Wissenschaften, Band 115 ]. We constantly 1 1. The textbook Real and cite definitions and results from Volume abstract analysis by E. HEWITT and K. R. STROMBERG [Berlin · Gottin gen ·Heidelberg: Springer-Verlag 1965], which appeared between the publication of the two volumes of this work, contains many standard facts from analysis. We use this book as a convenient reference for such facts, and denote it in the text by RAAA. Most readers will have only occasional need actually to read in RAAA. Our goal in this volume is to present the most important parts of harmonic analysis on compact groups and on locally compact Abelian groups. We deal with general locally compact groups only where they are the natural setting for what we are considering, or where one or another group provides a useful counterexample. Readers who are interested only in compact groups may read as follows: § 27, Appendix D, §§ 28-30 [omitting subheads (30.6)-(30.60)ifdesired], (31.22)-(31.25), §§ 32, 34-38, 44. Readers who are interested only in locally compact Abelian groups may read as follows: §§ 31-33, 39-42, selected Mis cellaneous Theorems and Examples in §§34-38. For all readers, § 43 is interesting but optional. Obviously we have not been able to cover all of harmonic analysis.
Book Synopsis Commutative Harmonic Analysis II by : V.P. Havin
Download or read book Commutative Harmonic Analysis II written by V.P. Havin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical harmonic analysis is an important part of modern physics and mathematics, comparable in its significance with calculus. Created in the 18th and 19th centuries as a distinct mathematical discipline it continued to develop, conquering new unexpected areas and producing impressive applications to a multitude of problems. It is widely understood that the explanation of this miraculous power stems from group theoretic ideas underlying practically everything in harmonic analysis. This book is an unusual combination of the general and abstract group theoretic approach with a wealth of very concrete topics attractive to everybody interested in mathematics. Mathematical literature on harmonic analysis abounds in books of more or less abstract or concrete kind, but the lucky combination as in this volume can hardly be found.
Book Synopsis A Course in Commutative Banach Algebras by : Eberhard Kaniuth
Download or read book A Course in Commutative Banach Algebras written by Eberhard Kaniuth and published by Springer Science & Business Media. This book was released on 2008-12-16 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Banach algebras are Banach spaces equipped with a continuous multipli- tion. In roughterms,there arethree types ofthem:algebrasofboundedlinear operators on Banach spaces with composition and the operator norm, al- bras consisting of bounded continuous functions on topological spaces with pointwise product and the uniform norm, and algebrasof integrable functions on locally compact groups with convolution as multiplication. These all play a key role in modern analysis. Much of operator theory is best approached from a Banach algebra point of view and many questions in complex analysis (such as approximation by polynomials or rational functions in speci?c - mains) are best understood within the framework of Banach algebras. Also, the study of a locally compact Abelian group is closely related to the study 1 of the group algebra L (G). There exist a rich literature and excellent texts on each single class of Banach algebras, notably on uniform algebras and on operator algebras. This work is intended as a textbook which provides a thorough introduction to the theory of commutative Banach algebras and stresses the applications to commutative harmonic analysis while also touching on uniform algebras. In this sense and purpose the book resembles Larsen’s classical text [75] which shares many themes and has been a valuable resource. However, for advanced graduate students and researchers I have covered several topics which have not been published in books before, including some journal articles.
Book Synopsis Real And Stochastic Analysis: Current Trends by : Malempati Madhusudana Rao
Download or read book Real And Stochastic Analysis: Current Trends written by Malempati Madhusudana Rao and published by World Scientific. This book was released on 2013-11-26 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the current status and research trends in Stochastic Analysis. Several new and emerging research areas are described in detail, highlighting the present outlook in Stochastic Analysis and its impact on abstract analysis. The book focuses on treating problems in areas that serve as a launching pad for continual research.
Book Synopsis A Course in Abstract Harmonic Analysis by : Gerald B. Folland
Download or read book A Course in Abstract Harmonic Analysis written by Gerald B. Folland and published by CRC Press. This book was released on 2016-02-03 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Canadian Mathematical Bulletin written by and published by . This book was released on 1971 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
