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Author :
Publisher : Elsevier
ISBN 13 : 008095412X
Total Pages : 285 pages
Book Rating : 4.0/5 (89 download)
Download or read book Algebraic Numbers and Harmonic Analysis written by and published by Elsevier. This book was released on 2000-04-01 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Numbers and Harmonic Analysis
Author : Yves Meyer
Publisher :
ISBN 13 : 9780720424522
Total Pages : 274 pages
Book Rating : 4.4/5 (245 download)
Download or read book Algebraic Numbers and Harmonic Analysis written by Yves Meyer and published by . This book was released on 1972-01-01 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diophantine approximations to real numbers. Some classical results in diophantine approximations. Measure-teoretical methods in diophantine approximations. Diophantine approximations and additive problems in locally compact abelian groups. Uniqueness of representation by trigonometric series. Problems on a-periodic trigonometric sums. Special trigonometric series (complex methods). Special trigonometric series (group-theoretic methods). Pisot numbers and spectral synthesis. Ultra-thin symmetric sets.
Author : Raphael Salem
Publisher :
ISBN 13 :
Total Pages : 98 pages
Book Rating : 4.:/5 (981 download)
Download or read book Algebraic Numbers and Fourier Analysis written by Raphael Salem and published by . This book was released on 1983 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Raphaël Salem
Publisher : Wadsworth Company
ISBN 13 :
Total Pages : 200 pages
Book Rating : 4.:/5 (321 download)
Download or read book Algebraic Numbers and Fourier Analysis written by Raphaël Salem and published by Wadsworth Company. This book was released on 1983 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Helmut Koch
Publisher : American Mathematical Soc.
ISBN 13 : 9780821820544
Total Pages : 390 pages
Book Rating : 4.8/5 (25 download)
Download or read book Number Theory written by Helmut Koch and published by American Mathematical Soc.. This book was released on 2000 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic number theory is one of the most refined creations in mathematics. It has been developed by some of the leading mathematicians of this and previous centuries. The primary goal of this book is to present the essential elements of algebraic number theory, including the theory of normal extensions up through a glimpse of class field theory. Following the example set for us by Kronecker, Weber, Hilbert and Artin, algebraic functions are handled here on an equal footing with algebraic numbers. This is done on the one hand to demonstrate the analogy between number fields and function fields, which is especially clear in the case where the ground field is a finite field. On the other hand, in this way one obtains an introduction to the theory of 'higher congruences' as an important element of 'arithmetic geometry'. Early chapters discuss topics in elementary number theory, such as Minkowski's geometry of numbers, public-key cryptography and a short proof of the Prime Number Theorem, following Newman and Zagier. Next, some of the tools of algebraic number theory are introduced, such as ideals, discriminants and valuations. These results are then applied to obtain results about function fields, including a proof of the Riemann-Roch Theorem and, as an application of cyclotomic fields, a proof of the first case of Fermat's Last Theorem. There are a detailed exposition of the theory of Hecke $L$-series, following Tate, and explicit applications to number theory, such as the Generalized Riemann Hypothesis. Chapter 9 brings together the earlier material through the study of quadratic number fields. Finally, Chapter 10 gives an introduction to class field theory. The book attempts as much as possible to give simple proofs. It can be used by a beginner in algebraic number theory who wishes to see some of the true power and depth of the subject. The book is suitable for two one-semester courses, with the first four chapters serving to develop the basic material. Chapters 6 through 9 could be used on their own as a second semester course.
Author : Bruce Lyndon Aubertin
Publisher :
ISBN 13 :
Total Pages : 250 pages
Book Rating : 4.:/5 (22 download)
Download or read book Algebraic Numbers and Harmonic Analysis in the P-series Case written by Bruce Lyndon Aubertin and published by . This book was released on 1986 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Valentin Blomer
Publisher : Springer Science & Business Media
ISBN 13 : 1461412196
Total Pages : 301 pages
Book Rating : 4.4/5 (614 download)
Download or read book Contributions in Analytic and Algebraic Number Theory written by Valentin Blomer and published by Springer Science & Business Media. This book was released on 2011-11-19 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text that comprises this volume is a collection of surveys and original works from experts in the fields of algebraic number theory, analytic number theory, harmonic analysis, and hyperbolic geometry. A portion of the collected contributions have been developed from lectures given at the "International Conference on the Occasion of the 60th Birthday of S. J. Patterson", held at the University Göttingen, July 27-29 2009. Many of the included chapters have been contributed by invited participants. This volume presents and investigates the most recent developments in various key topics in analytic number theory and several related areas of mathematics. The volume is intended for graduate students and researchers of number theory as well as applied mathematicians interested in this broad field.
Author : Dinakar Ramakrishnan
Publisher : Springer Science & Business Media
ISBN 13 : 1475730853
Total Pages : 372 pages
Book Rating : 4.4/5 (757 download)
Download or read book Fourier Analysis on Number Fields written by Dinakar Ramakrishnan and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasising harmonic analysis on topological groups. The main goal is to cover John Tates visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries -- technical prerequisites that are often foreign to the typical, more algebraically inclined number theorist. While most of the existing treatments of Tates thesis are somewhat terse and less than complete, the intent here is to be more leisurely, more comprehensive, and more comprehensible. While the choice of objects and methods is naturally guided by specific mathematical goals, the approach is by no means narrow. In fact, the subject matter at hand is germane not only to budding number theorists, but also to students of harmonic analysis or the representation theory of Lie groups. The text addresses students who have taken a year of graduate-level course in algebra, analysis, and topology. Moreover, the work will act as a good reference for working mathematicians interested in any of these fields.
Author : Marie J. Bertin
Publisher : Birkhäuser
ISBN 13 : 3034886322
Total Pages : 297 pages
Book Rating : 4.0/5 (348 download)
Download or read book Pisot and Salem Numbers written by Marie J. Bertin and published by Birkhäuser. This book was released on 2012-12-06 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: the attention of The publication of Charles Pisot's thesis in 1938 brought to the mathematical community those marvelous numbers now known as the Pisot numbers (or the Pisot-Vijayaraghavan numbers). Although these numbers had been discovered earlier by A. Thue and then by G. H. Hardy, it was Pisot's result in that paper of 1938 that provided the link to harmonic analysis, as discovered by Raphael Salem and described in a series of papers in the 1940s. In one of these papers, Salem introduced the related class of numbers, now universally known as the Salem numbers. These two sets of algebraic numbers are distinguished by some striking arith metic properties that account for their appearance in many diverse areas of mathematics: harmonic analysis, ergodic theory, dynamical systems and alge braic groups. Until now, the best known and most accessible introduction to these num bers has been the beautiful little monograph of Salem, Algebraic Numbers and Fourier Analysis, first published in 1963. Since the publication of Salem's book, however, there has been much progress in the study of these numbers. Pisot had long expressed the desire to publish an up-to-date account of this work, but his death in 1984 left this task unfulfilled.
Author : Robert S. Doran, Paul J. Sally, Jr., and Loren Spice
Publisher : American Mathematical Soc.
ISBN 13 : 0821874039
Total Pages : 294 pages
Book Rating : 4.8/5 (218 download)
Download or read book Harmonic Analysis on Reductive, $p$-adic Groups written by Robert S. Doran, Paul J. Sally, Jr., and Loren Spice and published by American Mathematical Soc.. This book was released on 2011 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Audrey Terras
Publisher : Springer Science & Business Media
ISBN 13 : 1461251281
Total Pages : 353 pages
Book Rating : 4.4/5 (612 download)
Download or read book Harmonic Analysis on Symmetric Spaces and Applications I written by Audrey Terras and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its beginnings with Fourier (and as far back as the Babylonian astron omers), harmonic analysis has been developed with the goal of unraveling the mysteries of the physical world of quasars, brain tumors, and so forth, as well as the mysteries of the nonphysical, but no less concrete, world of prime numbers, diophantine equations, and zeta functions. Quoting Courant and Hilbert, in the preface to the first German edition of Methods of Mathematical Physics: "Recent trends and fashions have, however, weakened the connection between mathematics and physics. " Such trends are still in evidence, harmful though they may be. My main motivation in writing these notes has been a desire to counteract this tendency towards specialization and describe appli cations of harmonic analysis in such diverse areas as number theory (which happens to be my specialty), statistics, medicine, geophysics, and quantum physics. I remember being quite surprised to learn that the subject is useful. My graduate eduation was that of the 1960s. The standard mathematics graduate course proceeded from Definition 1. 1. 1 to Corollary 14. 5. 59, with no room in between for applications, motivation, history, or references to related work. My aim has been to write a set of notes for a very different sort of course.
Author : George W. Mackey
Publisher : American Mathematical Soc.
ISBN 13 : 9780821890448
Total Pages : 386 pages
Book Rating : 4.8/5 (94 download)
Download or read book The Scope and History of Commutative and Noncommutative Harmonic Analysis written by George W. Mackey and published by American Mathematical Soc.. This book was released on 2005-04-08 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: ''When I was invited to speak at the conference on the history of analysis given at Rice University [in 1977], I decided that it might be interesting to review the history of mathematics and physics in the last three hundred years or so with heavy emphasis on those parts in which harmonic analysis had played a decisive or at least a major role. I was pleased and somewhat astonished to find how much of both subjects could be included under this rubric ... The picture that gradually emerged as the various details fell into place was one that I found very beautiful, and the process of seeing it do so left me in an almost constant state of euphoria. I would like to believe that others can be led to see this picture by reading my paper, and to facilitate this I have included a large number of short expositions of topics which are not widely understood by non-specialists.'' --from the Preface This volume, containing the paper mentioned above as well as five other reprinted papers by Mackey, presents a sweeping view of the importance, utility, and beauty of harmonic analysis and its connections to other areas of mathematics and science. A seventh paper, written exclusively for this volume, attempts to unify certain themes that emerged after major discoveries in 1967 and 1968 in the areas of Lie algebras, strong interaction physics, statistical mechanics, and nonlinear partial differential equations--discoveries that may at first glance appear to be independent, but which are in fact deeply interrelated. Information for our distributors: Copublished with the London Mathematical Society beginning with volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.
Author : Hugh L. Montgomery
Publisher : American Mathematical Soc.
ISBN 13 : 1470424444
Total Pages : 242 pages
Book Rating : 4.4/5 (74 download)
Download or read book Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis written by Hugh L. Montgomery and published by American Mathematical Soc.. This book was released on 1994 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains lectures presented by Hugh L. Montgomery at the NSF-CBMS Regional Conference held at Kansas State University in May 1990. The book focuses on important topics in analytic number theory that involve ideas from harmonic analysis. One valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature. This book would be an excellent resource for harmonic analysts interested in moving into research in analytic number theory. In addition, it is suitable as a textbook in an advanced graduate topics course in nu.
Author : Carl L. DeVito
Publisher : Jones & Bartlett Learning
ISBN 13 : 9780763738938
Total Pages : 240 pages
Book Rating : 4.7/5 (389 download)
Download or read book Harmonic Analysis written by Carl L. DeVito and published by Jones & Bartlett Learning. This book was released on 2007 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Mathematics
Author : Clay Mathematics Institute. Summer School
Publisher : American Mathematical Soc.
ISBN 13 : 9780821838440
Total Pages : 708 pages
Book Rating : 4.8/5 (384 download)
Download or read book Harmonic Analysis, the Trace Formula, and Shimura Varieties written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2005 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: Langlands program proposes fundamental relations that tie arithmetic information from number theory and algebraic geometry with analytic information from harmonic analysis and group representations. This title intends to provide an entry point into this exciting and challenging field.
Author : Weiyi Su
Publisher : World Scientific
ISBN 13 : 9813200529
Total Pages : 331 pages
Book Rating : 4.8/5 (132 download)
Download or read book Harmonic Analysis And Fractal Analysis Over Local Fields And Applications written by Weiyi Su and published by World Scientific. This book was released on 2017-08-17 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a monograph on harmonic analysis and fractal analysis over local fields. It can also be used as lecture notes/textbook or as recommended reading for courses on modern harmonic and fractal analysis. It is as reliable as Fourier Analysis on Local Fields published in 1975 which is regarded as the first monograph in this research field.The book is self-contained, with wide scope and deep knowledge, taking modern mathematics (such as modern algebra, point set topology, functional analysis, distribution theory, and so on) as bases. Specially, fractal analysis is studied in the viewpoint of local fields, and fractal calculus is established by pseudo-differential operators over local fields. A frame of fractal PDE is constructed based on fractal calculus instead of classical calculus. On the other hand, the author does his best to make those difficult concepts accessible to readers, illustrate clear comparison between harmonic analysis on Euclidean spaces and that on local fields, and at the same time provide motivations underlying the new concepts and techniques. Overall, it is a high quality, up to date and valuable book for interested readers.
Author : Garth Warner
Publisher : Springer Science & Business Media
ISBN 13 : 364250275X
Total Pages : 545 pages
Book Rating : 4.6/5 (425 download)
Download or read book Harmonic Analysis on Semi-Simple Lie Groups I written by Garth Warner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: The representation theory of locally compact groups has been vig orously developed in the past twenty-five years or so; of the various branches of this theory, one of the most attractive (and formidable) is the representation theory of semi-simple Lie groups which, to a great extent, is the creation of a single man: Harish-Chandra. The chief objective of the present volume and its immediate successor is to provide a reasonably self-contained introduction to Harish-Chandra's theory. Granting cer tain basic prerequisites (cf. infra), we have made an effort to give full details and complete proofs of the theorems on which the theory rests. The structure of this volume and its successor is as follows. Each book is divided into chapters; each chapter is divided into sections; each section into numbers. We then use the decimal system of reference; for example, 1. 3. 2 refers to the second number in the third section of the first chapter. Theorems, Propositions, Lemmas, and Corollaries are listed consecutively throughout any given number. Numbers which are set in fine print may be omitted at a first reading. There are a variety of Exam ples scattered throughout the text; the reader, if he is so inclined, can view them as exercises ad libitum. The Appendices to the text collect certain ancillary results which will be used on and off in the systematic exposi tion; a reference of the form A2.
