a panorama of harmonic analysis carus mathematical monographs

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A Panorama Of Harmonic Analysis

Author : Steven Krantz
ISBN : 0883850311
Genre : Mathematics
File Size : 65. 75 MB
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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
ISBN : 9780821875667
Genre : Mathematics
File Size : 75. 74 MB
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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
ISBN : 9781475738346
Genre : Mathematics
File Size : 50. 27 MB
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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
ISBN : 0883850362
Genre : Mathematics
File Size : 24. 39 MB
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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
ISBN : STANFORD:36105111802596
Genre : Mathematics
File Size : 42. 61 MB
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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.

Crux Mathematicorum With Mathematical Mayhem

Author :
ISBN : UOM:39015051268749
Genre : Mathematics
File Size : 52. 76 MB
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The Taming Of Chance

Author : Ian Hacking
ISBN : 0521388848
Genre : History
File Size : 77. 78 MB
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This book combines detailed scientific historical research with characteristic philosophic breadth and verve.

Number Theory Fourier Analysis And Geometric Discrepancy

Author : Giancarlo Travaglini
ISBN : 9781107044036
Genre : Mathematics
File Size : 42. 54 MB
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"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 Sensual Quadratic Form

Author : John Horton Conway
ISBN : 0883850303
Genre : Mathematics
File Size : 55. 87 MB
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Real mathematics without theorems by John Conway.

Math Through The Ages

Author : William P. Berlinghoff
ISBN : 0883857367
Genre : Mathematics
File Size : 34. 48 MB
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An informal and accessible overview of the history of mathematics.

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