Harmonic Analysis

e-books in Harmonic Analysis category

Introduction to the Theory of Fourier's Series and IntegralsIntroduction to the Theory of Fourier's Series and Integrals
by H. S. Carslaw - Macmillan and co. , 1921
An introductory explanation of the theory of Fourier's series. It covers tests for uniform convergence of series, a thorough treatment of term-by-term integration and second theorem of mean value, enlarged sets of examples on infinite series, etc.
Contributions to Fourier AnalysisContributions to Fourier Analysis
by A. Zygmund, et al. - Princeton University Press , 1950
In the theory of convergence and summability, emphasis is placed on the phenomenon of localization whenever such occurs, and in the present paper a certain aspect of this phenomenon will be studied for the problem of best approximation as well.
Spherical Harmonics in p DimensionsSpherical Harmonics in p Dimensions
by Christopher Frye, Costas J. Efthimiou - arXiv , 2012
The authors prepared this booklet in order to make several useful topics from the theory of special functions, in particular the spherical harmonics and Legendre polynomials for any dimension, available to physics or mathematics undergraduates.

Lectures on Harmonic AnalysisLectures on Harmonic Analysis
by Thomas Wolff - American Mathematical Society , 2003
An inside look at the techniques used and developed by the author. The book is based on a graduate course on Fourier analysis he taught at Caltech. It demonstrates how harmonic analysis can provide penetrating insights into deep aspects of analysis.
Harmonic AnalysisHarmonic Analysis
by S.R.S. Varadhan - New York University , 2000
Fourier Series of a periodic function. Fejer kernel. Convergence Properties. Convolution and Fourier Series. Heat Equation. Diagonalization of convolution operators. Fourier Transforms on Rd. Multipliers and singular integral operators. etc...
Harmonic AnalysisHarmonic Analysis
by Russell Brown - University of Kentucky , 2009
These notes are intended for a course in harmonic analysis on Rn for graduate students. The background for this course is a course in real analysis which covers measure theory and the basic facts of life related to Lp spaces.
Nonlinear Fourier AnalysisNonlinear Fourier Analysis
by Terence Tao, Christoph Thiele - arXiv , 2012
The nonlinear Fourier transform is the map from the potential of a one dimensional discrete Dirac operator to the transmission and reflection coefficients thereof. Emphasis is on this being a nonlinear variant of the classical Fourier series.
Lectures on Topics in Mean Periodic Functions and the Two-Radius TheoremLectures on Topics in Mean Periodic Functions and the Two-Radius Theorem
by J. Delsarte - Tata Institute of Fundamental Research , 1961
Subjects treated: transmutations of singular differential operators of the second order in the real case; new results on the theory of mean periodic functions; proof of the two-radius theorem, which is the converse of Gauss's classical theorem.
Lectures on Potential TheoryLectures on Potential Theory
by M. Brelot - Tata Institute of Fundamental Research , 1967
In the following we shall develop some results of the axiomatic approaches to potential theory principally some convergence theorems; they may be used as fundamental tools and applied to classical case as we shall indicate sometimes.
Lectures on Mean Periodic FunctionsLectures on Mean Periodic Functions
by J.P. Kahane - Tata Institute of Fundamental Research , 1959
Mean periodic functions are a generalization of periodic functions. The book considers questions such as Fourier-series, harmonic analysis, the problems of uniqueness, approximation and quasi-analyticity, as problems on mean periodic functions.
Notes on Harmonic AnalysisNotes on Harmonic Analysis
by George Benthien , 2006
Tutorial discussing some of the numerical aspects of practical harmonic analysis. Topics include Historical Background, Fourier Series and Integral Approximations, Convergence Improvement, Differentiation of Fourier Series and Sigma Factors, etc.
Harmonic Function TheoryHarmonic Function Theory
by Sheldon Axler, Paul Bourdon, Wade Ramey - Springer , 2001
A book about harmonic functions in Euclidean space. Readers with a background in real and complex analysis at the beginning graduate level will feel comfortable with the text. The authors have taken care to motivate concepts and simplify proofs.
Chebyshev and Fourier Spectral MethodsChebyshev and Fourier Spectral Methods
by John P. Boyd - Dover Publications , 2001
The text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, cardinal functions, etc.
Linear Partial Differential Equations and Fourier TheoryLinear Partial Differential Equations and Fourier Theory
by Marcus Pivato - Cambridge University Press , 2005
Textbook for an introductory course on linear partial differential equations and boundary value problems. It also provides introduction to basic Fourier analysis and functional analysis. Written for third-year undergraduates in mathematical sciences.