## e-books in Harmonic Analysis category

**Introduction 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.

(

**550**views)

**Contributions 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.

(

**2139**views)

**Spherical 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.

(

**4157**views)

**Lectures 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.

(

**5111**views)

**Harmonic 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...

(

**4683**views)

**Harmonic 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.

(

**4441**views)

**Nonlinear 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.

(

**4393**views)

**Lectures 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.

(

**4181**views)

**Lectures 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.

(

**4132**views)

**Lectures 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.

(

**4338**views)

**Notes 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.

(

**5695**views)

**An elementary treatise on Fourier's series and spherical, cylindrical, and ellipsoidal harmonics**

by

**William Elwood Byerly**-

**Ginn and company**,

**1893**

From the table of contents: Development in Trigonometric Series; Convergence of Fourier's Series; Solution of Problems in Physics by the Aid of Fourier's Integrals and Fourier's Series; Zonal Harmonics; Spherical Harmonics; Cylindrical Harmonics; ...

(

**10093**views)

**Fourier Series and Systems of Differential Equations and Eigenvalue Problems**

by

**Leif Mejlbro**-

**BookBoon**,

**2007**

This volume gives some guidelines for solving problems in the theories of Fourier series and Systems of Differential Equations and eigenvalue problems. It can be used as a supplement to the textbooks in which one can find all the necessary proofs.

(

**8037**views)

**Harmonic 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.

(

**8614**views)

**Chebyshev 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.

(

**12731**views)

**Linear 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.

(

**21828**views)