A Panorama of Harmonic Analysis

Author: Steven Krantz
Publisher: Cambridge University Press
ISBN: 0883850311
Release Date: 1999-09-02
Genre: Mathematics

Tracing a path from the earliest beginnings of Fourier series through to the latest research A Panorama of Harmonic Analysis discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space. The climax is a consideration of ideas from the point of view of spaces of homogeneous type, which culminates in a discussion of wavelets. This book is intended for graduate students and advanced undergraduates, and mathematicians of whatever background who want a clear and concise overview of the subject of commutative harmonic analysis.

Harmonic Analysis

Author: María Cristina Pereyra
Publisher: American Mathematical Soc.
ISBN: 9780821875667
Release Date: 2012
Genre: Mathematics

In the last 200 years, harmonic analysis has been one of the most influential bodies of mathematical ideas, having been exceptionally significant both in its theoretical implications and in its enormous range of applicability throughout mathematics, science, and engineering. In this book, the authors convey the remarkable beauty and applicability of the ideas that have grown from Fourier theory. They present for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization). While concentrating on the Fourier and Haar cases, the book touches on aspects of the world that lies between these two different ways of decomposing functions: time-frequency analysis (wavelets). Both finite and continuous perspectives are presented, allowing for the introduction of discrete Fourier and Haar transforms and fast algorithms, such as the Fast Fourier Transform (FFT) and its wavelet analogues. The approach combines rigorous proof, inviting motivation, and numerous applications. Over 250 exercises are included in the text. Each chapter ends with ideas for projects in harmonic analysis that students can work on independently. This book is published in cooperation with IAS/Park City Mathematics Institute.

A First Course in Harmonic Analysis

Author: Anton Deitmar
Publisher: Springer Science & Business Media
ISBN: 9781475738346
Release Date: 2013-04-17
Genre: Mathematics

This book introduces harmonic analysis at an undergraduate level. In doing so it covers Fourier analysis and paves the way for Poisson Summation Formula. Another central feature is that is makes the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The final goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.

A Tour Through Mathematical Logic

Author: Robert S. Wolf
Publisher: MAA
ISBN: 0883850362
Release Date: 2005-03-10
Genre: Mathematics

A guide that any interested reader with some post-calculus experience in mathematics can read, enjoy, and learn from.

Classical and Modern Fourier Analysis

Author: Loukas Grafakos
Publisher: Prentice Hall
ISBN: STANFORD:36105111802596
Release Date: 2004
Genre: Mathematics

For graduate-level courses in Fourier or harmonic analysis. Designed specifically for students (rather than researchers), this introduction to Fourier Analysis starts where the real and complex first-year graduate classes end.

Contemporary Authors

Author: Gale Group
Publisher: Gale Cengage
ISBN: 0787620025
Release Date: 1999
Genre: Biography & Autobiography

Since 1962, Contemporary Authors has been an authoritative and comprehensive source of bibliographic and biographical information on important authors of the 20th century. This reference allows the user to access entries by author name, title of work or specific personal data.

Number Theory Fourier Analysis and Geometric Discrepancy

Author: Giancarlo Travaglini
Publisher: Cambridge University Press
ISBN: 9781107044036
Release Date: 2014-06-12
Genre: Mathematics

"The first part of this book is dedicated to the first goal. The reader will find some topics typically presented in introductory books on Number Theory: factorization, arithmetic functions and integer points, congruences and cryptography, quadratic reciprocity, and sums of two and four squares. Starting from the first few pages we introduce some simple and captivating findings, such as Chebyshev's theorem and the elementary results for the Gauss circle problem and for the Dirichlet divisor problem, which may lead the reader to a deeper study of Number Theory, particularly students who are interested in Calculus and Analysis"--

The Proof is in the Pudding

Author: Steven G. Krantz
Publisher: Springer Science & Business Media
ISBN: 0387487441
Release Date: 2011-05-13
Genre: Mathematics

This text explores the many transformations that the mathematical proof has undergone from its inception to its versatile, present-day use, considering the advent of high-speed computing machines. Though there are many truths to be discovered in this book, by the end it is clear that there is no formalized approach or standard method of discovery to date. Most of the proofs are discussed in detail with figures and equations accompanying them, allowing both the professional mathematician and those less familiar with mathematics to derive the same joy from reading this book.

Books in Print

ISBN: UOM:39015049090585
Release Date: 2001
Genre: American literature

Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

The Taming of Chance

Author: Ian Hacking
Publisher: Cambridge University Press
ISBN: 0521388848
Release Date: 1990-08-31
Genre: History

This book combines detailed scientific historical research with characteristic philosophic breadth and verve.

Math Through the Ages

Author: William P. Berlinghoff
Publisher: MAA
ISBN: 0883857367
Release Date: 2004
Genre: Mathematics

An informal and accessible overview of the history of mathematics.