Fourier Analysis On Local Fields Mn 15
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Author |
: M. H. Taibleson |
Publisher |
: Princeton University Press |
Total Pages |
: 308 |
Release |
: 2015-03-08 |
ISBN-10 |
: 9781400871339 |
ISBN-13 |
: 1400871336 |
Rating |
: 4/5 (39 Downloads) |
Synopsis Fourier Analysis on Local Fields. (MN-15) by : M. H. Taibleson
This book presents a development of the basic facts about harmonic analysis on local fields and the n-dimensional vector spaces over these fields. It focuses almost exclusively on the analogy between the local field and Euclidean cases, with respect to the form of statements, the manner of proof, and the variety of applications. The force of the analogy between the local field and Euclidean cases rests in the relationship of the field structures that underlie the respective cases. A complete classification of locally compact, non-discrete fields gives us two examples of connected fields (real and complex numbers); the rest are local fields (p-adic numbers, p-series fields, and their algebraic extensions). The local fields are studied in an effort to extend knowledge of the reals and complexes as locally compact fields. The author's central aim has been to present the basic facts of Fourier analysis on local fields in an accessible form and in the same spirit as in Zygmund's Trigonometric Series (Cambridge, 1968) and in Introduction to Fourier Analysis on Euclidean Spaces by Stein and Weiss (1971). Originally published in 1975. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author |
: Biswaranjan Behera |
Publisher |
: Springer Nature |
Total Pages |
: 345 |
Release |
: 2022-01-01 |
ISBN-10 |
: 9789811678813 |
ISBN-13 |
: 9811678812 |
Rating |
: 4/5 (13 Downloads) |
Synopsis Wavelet Analysis on Local Fields of Positive Characteristic by : Biswaranjan Behera
This book discusses the theory of wavelets on local fields of positive characteristic. The discussion starts with a thorough introduction to topological groups and local fields. It then provides a proof of the existence and uniqueness of Haar measures on locally compact groups. It later gives several examples of locally compact groups and describes their Haar measures. The book focuses on multiresolution analysis and wavelets on a local field of positive characteristic. It provides characterizations of various functions associated with wavelet analysis such as scaling functions, wavelets, MRA-wavelets and low-pass filters. Many other concepts which are discussed in details are biorthogonal wavelets, wavelet packets, affine and quasi-affine frames, MSF multiwavelets, multiwavelet sets, generalized scaling sets, scaling sets, unconditional basis properties of wavelets and shift invariant spaces.
Author |
: Bao Luong |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 167 |
Release |
: 2009-08-14 |
ISBN-10 |
: 9780817649166 |
ISBN-13 |
: 0817649166 |
Rating |
: 4/5 (66 Downloads) |
Synopsis Fourier Analysis on Finite Abelian Groups by : Bao Luong
This unified, self-contained book examines the mathematical tools used for decomposing and analyzing functions, specifically, the application of the [discrete] Fourier transform to finite Abelian groups. With countless examples and unique exercise sets at the end of each section, Fourier Analysis on Finite Abelian Groups is a perfect companion to a first course in Fourier analysis. This text introduces mathematics students to subjects that are within their reach, but it also has powerful applications that may appeal to advanced researchers and mathematicians. The only prerequisites necessary are group theory, linear algebra, and complex analysis.
Author |
: Keiko Fujita |
Publisher |
: World Scientific |
Total Pages |
: 339 |
Release |
: 2002-12-12 |
ISBN-10 |
: 9789814487504 |
ISBN-13 |
: 9814487503 |
Rating |
: 4/5 (04 Downloads) |
Synopsis Microlocal Analysis And Complex Fourier Analysis by : Keiko Fujita
This book is a collection of original papers on microlocal analysis, Fourier analysis in the complex domain, generalized functions and related topics. Most of the papers originate from the talks given at the conference “Prospects of Generalized Functions” (in November, 2001 at RIMS, Kyoto). Reflecting the fact that the papers, except M Morimoto's one, are dedicated to Mitsuo Morimoto, the subjects considered in this book are interdisciplinary, just as Morimoto's works are. The historical backgrounds of the subjects are also discussed in depth in some contributions. Thus, this book should be valuable not only to the specialists in the fields, but also to those who are interested in the history of modern mathematics such as distributions and hyperfunctions.
Author |
: Dinakar Ramakrishnan |
Publisher |
: Springer |
Total Pages |
: |
Release |
: 2002-03-01 |
ISBN-10 |
: 3540780890 |
ISBN-13 |
: 9783540780892 |
Rating |
: 4/5 (90 Downloads) |
Synopsis Fourier Analysis on Number Fields by : Dinakar Ramakrishnan
Author |
: David W. Kammler |
Publisher |
: Cambridge University Press |
Total Pages |
: 39 |
Release |
: 2008-01-17 |
ISBN-10 |
: 9781139469036 |
ISBN-13 |
: 1139469037 |
Rating |
: 4/5 (36 Downloads) |
Synopsis A First Course in Fourier Analysis by : David W. Kammler
This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.
Author |
: Robert J Marks II |
Publisher |
: Oxford University Press |
Total Pages |
: 799 |
Release |
: 2009-01-08 |
ISBN-10 |
: 9780198044307 |
ISBN-13 |
: 0198044305 |
Rating |
: 4/5 (07 Downloads) |
Synopsis Handbook of Fourier Analysis & Its Applications by : Robert J Marks II
Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas. In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes. This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal processing and related multidimensional transform theory, and quantum physics to elementary deterministic finance and even the foundations of western music theory. As a definitive text on Fourier Analysis, Handbook of Fourier Analysis and Its Applications is meant to replace several less comprehensive volumes on the subject, such as Processing of Multifimensional Signals by Alexandre Smirnov, Modern Sampling Theory by John J. Benedetto and Paulo J.S.G. Ferreira, Vector Space Projections by Henry Stark and Yongyi Yang and Fourier Analysis and Imaging by Ronald N. Bracewell. In addition to being primarily used as a professional handbook, it includes sample problems and their solutions at the end of each section and thus serves as a textbook for advanced undergraduate students and beginning graduate students in courses such as: Multidimensional Signals and Systems, Signal Analysis, Introduction to Shannon Sampling and Interpolation Theory, Random Variables and Stochastic Processes, and Signals and Linear Systems.
Author |
: Loren Argabright |
Publisher |
: |
Total Pages |
: |
Release |
: 1971 |
ISBN-10 |
: OCLC:856874547 |
ISBN-13 |
: |
Rating |
: 4/5 (47 Downloads) |
Synopsis Fourier Analysis of Unbounded Measures on Locally Compact Abelian Groups by : Loren Argabright
Author |
: Sir M. J. Lighthill |
Publisher |
: Cambridge University Press |
Total Pages |
: 112 |
Release |
: 1958 |
ISBN-10 |
: 0521091284 |
ISBN-13 |
: 9780521091282 |
Rating |
: 4/5 (84 Downloads) |
Synopsis An Introduction to Fourier Analysis and Generalised Functions by : Sir M. J. Lighthill
"Clearly and attractively written, but without any deviation from rigorous standards of mathematical proof...." Science Progress
Author |
: Walter Rudin |
Publisher |
: John Wiley & Sons |
Total Pages |
: 306 |
Release |
: 1962-01-15 |
ISBN-10 |
: UOM:39015000491434 |
ISBN-13 |
: |
Rating |
: 4/5 (34 Downloads) |
Synopsis Fourier Analysis on Groups by : Walter Rudin
In the late 1950s, many of the more refined aspects of Fourier analysis were transferred from their original settings (the unit circle, the integers, the real line) to arbitrary locally compact abelian (LCA) groups. Rudin's book, published in 1962, was the first to give a systematic account of these developments and has come to be regarded as a classic in the field. The basic facts concerning Fourier analysis and the structure of LCA groups are proved in the opening chapters, in order to make the treatment relatively self-contained.