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e-books in this category

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.
(1190 views)

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.
(2276 views)

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...
(2057 views)

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.
(2059 views)

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.
(2101 views)

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.
(1663 views)

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.
(2049 views)

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.
(2028 views)

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.
(3233 views)

An elementary treatise on Fourier's series and spherical, cylindrical, and ellipsoidal harmonicsAn 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; ...
(6520 views)

Fourier Series and Systems of Differential Equations and Eigenvalue ProblemsFourier 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.
(5602 views)

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.
(5910 views)

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.
(9103 views)

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.
(8572 views)