e-books in Harmonic Analysis category
Real Harmonic Analysisby Pascal Auscher, Lashi Bandara - ANU eView , 2012
This book presents the material covered in graduate lectures delivered in 2010. Moving from the classical periodic setting to the real line, then to, nowadays, sets with minimal structures, the theory has reached a high level of applicability.
(6214 views)
Introduction to the Theory of Fourier's Series and Integralsby 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.
(7047 views)
Contributions to Fourier Analysisby 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.
(8039 views)
Spherical Harmonics in p Dimensionsby 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.
(10537 views)
Lectures on Harmonic Analysisby 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.
(11476 views)
Harmonic Analysisby S.R.S. Varadhan - New York University , 2019
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...
(10601 views)
Harmonic Analysisby 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.
(10545 views)
Nonlinear Fourier Analysisby 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.
(9622 views)
Lectures on Topics in Mean Periodic Functions and the Two-Radius Theoremby 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.
(9143 views)
Lectures on Potential Theoryby 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.
(9674 views)
Lectures on Mean Periodic Functionsby 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.
(9590 views)
Notes on Harmonic Analysisby 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.
(11685 views)
An elementary treatise on Fourier's series and spherical, cylindrical, and ellipsoidal harmonicsby 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; ...
(17590 views)
Fourier Series and Systems of Differential Equations and Eigenvalue Problemsby 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.
(13864 views)
Harmonic Function Theoryby 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.
(14384 views)
Chebyshev and Fourier Spectral Methodsby 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.
(19905 views)
Linear Partial Differential Equations and Fourier Theoryby 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.
(29264 views)