Spherical Harmonics

Author : Kendall Atkinson,Weimin Han
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 55,6 Mb
Release : 2012-02-17
Category : Mathematics
ISBN : 9783642259821

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Spherical Harmonics and Approximations on the Unit Sphere: An Introduction by Kendall Atkinson,Weimin Han Pdf

These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well as an overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical integration over the unit sphere. The notes are intended for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations on the unit sphere, especially on the unit sphere in three-dimensional Euclidean space. Some related work for approximation on the unit disk in the plane is also briefly discussed, with results being generalizable to the unit ball in more dimensions.

Author : H. Groemer
Publisher : Cambridge University Press
Page : 343 pages
File Size : 45,9 Mb
Release : 1996-09-13
Category : Mathematics
ISBN : 9780521473187

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Geometric Applications of Fourier Series and Spherical Harmonics by H. Groemer Pdf

This book provides a comprehensive presentation of geometric results, primarily from the theory of convex sets, that have been proved by the use of Fourier series or spherical harmonics. An important feature of the book is that all necessary tools from the classical theory of spherical harmonics are presented with full proofs. These tools are used to prove geometric inequalities, stability results, uniqueness results for projections and intersections by hyperplanes or half-spaces and characterisations of rotors in convex polytopes. Again, full proofs are given. To make the treatment as self-contained as possible the book begins with background material in analysis and the geometry of convex sets. This treatise will be welcomed both as an introduction to the subject and as a reference book for pure and applied mathematics.

Author : Claus Müller
Publisher : Springer
Page : 50 pages
File Size : 44,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540371748

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Spherical Harmonics by Claus Müller Pdf

Author : Feng Dai,Yuan Xu
Publisher : Springer Science & Business Media
Page : 447 pages
File Size : 40,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781461466604

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Approximation Theory and Harmonic Analysis on Spheres and Balls by Feng Dai,Yuan Xu Pdf

This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.

Author : Kendall Atkinson,Weimin Han
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 54,5 Mb
Release : 2012-02-17
Category : Mathematics
ISBN : 9783642259838

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Spherical Harmonics and Approximations on the Unit Sphere: An Introduction by Kendall Atkinson,Weimin Han Pdf

These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well as an overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical integration over the unit sphere. The notes are intended for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations on the unit sphere, especially on the unit sphere in three-dimensional Euclidean space. Some related work for approximation on the unit disk in the plane is also briefly discussed, with results being generalizable to the unit ball in more dimensions.

Author : Costas Efthimiou,Christopher Frye
Publisher : World Scientific
Page : 156 pages
File Size : 46,5 Mb
Release : 2014-03-07
Category : Mathematics
ISBN : 9789814596718

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Spherical Harmonics in p Dimensions by Costas Efthimiou,Christopher Frye Pdf

The current book makes several useful topics from the theory of special functions, in particular the theory of spherical harmonics and Legendre polynomials in arbitrary dimensions, available to undergraduates studying physics or mathematics. With this audience in mind, nearly all details of the calculations and proofs are written out, and extensive background material is covered before exploring the main subject matter. Contents:Introduction and MotivationWorking in p DimensionsOrthogonal PolynomialsSpherical Harmonics in p DimensionsSolutions to Problems Readership: Undergraduate and graduate students in mathematical physics and differential equations. Key Features:Accessible to everyone (including undergraduate students who have some knowledge in mathematics)Presents a topic that, although well-studied, is not widely disseminated in booksSolutions to all end-of-chapter problems with all the necessary details are given in the final chapter of the bookKeywords:Spherical Harmonics;Special Functions;Mathematical Physics;Green's Functions;Legendre Polynomials

Author : Norman M. Ferrers
Publisher : Unknown
Page : 212 pages
File Size : 42,6 Mb
Release : 1877
Category : Electronic
ISBN : BSB:BSB11369193

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An Elementary Treatise on Spherical Harmonics, and Subjects Connected with Them by Norman M. Ferrers Pdf

Author : E. W. Hobson
Publisher : CUP Archive
Page : 520 pages
File Size : 51,6 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 8210379456XXX

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the theory of spherical and ellipsoidal harmonics by E. W. Hobson Pdf

Author : Keith L. McDonald
Publisher : Unknown
Page : 80 pages
File Size : 40,9 Mb
Release : 1969
Category : Geomagnetism
ISBN : PSU:000072011317

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Tables of Integrals for the Spherical Harmonic Expansion of the Hydromagnetic Equations by Keith L. McDonald Pdf

Author : Anonim
Publisher : Academic Press
Page : 349 pages
File Size : 46,6 Mb
Release : 1949-01-01
Category : Mathematics
ISBN : 9780080873091

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Partial Differential Equations in Physics by Anonim Pdf

The topic with which I regularly conclude my six-term series of lectures in Munich is the partial differential equations of physics. We do not really deal with mathematical physics, but with physical mathematics; not with the mathematical formulation of physical facts, but with the physical motivation of mathematical methods. The oftmentioned “prestabilized harmony between what is mathematically interesting and what is physically important is met at each step and lends an esthetic - I should like to say metaphysical -- attraction to our subject. The problems to be treated belong mainly to the classical matherhatical literature, as shown by their connection with the names of Laplace, Fourier, Green, Gauss, Riemann, and William Thomson. In order to show that these methods are adequate to deal with actual problems, we treat the propagation of radio waves in some detail in Chapter VI.

Author : William Elwood Byerly
Publisher : Cosimo, Inc.
Page : 301 pages
File Size : 54,6 Mb
Release : 2007-01-01
Category : Science
ISBN : 9781602063051

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An Elementary Treatise on Fourier's Series and Spherical, Cylindric, and Ellipsoidal Harmonics by William Elwood Byerly Pdf

First published in 1893, Byerly's classic treatise on Fourier's series and spherical, cylindrical, and ellipsoidal harmonics has been used in classrooms for well over a century. This practical exposition acts as a primer for fields such as wave mechanics, advanced engineering, and mathematical physics. Topics covered include: . development in trigonometric series . convergence on 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 (Bessel's functions) . and more. Containing 190 exercises and a helpful appendix, this reissue of Fourier's Series will be welcomed by students of higher mathematics everywhere. American mathematician WILLIAM ELWOOD BYERLY (1849-1935) also wrote Elements of Differential Calculus (1879) and Elements of Integral Calculus (1881).

Author : Wolfgang Sternberg,Turner L. Smith
Publisher : Unknown
Page : 0 pages
File Size : 51,8 Mb
Release : 1964
Category : Electronic
ISBN : OCLC:1067415349

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The Theory of Potential and Spherical Harmonics by Wolfgang Sternberg,Turner L. Smith Pdf

Author : Wolfgang J. Sternberg,Turner Linn Smith
Publisher : Unknown
Page : 332 pages
File Size : 42,9 Mb
Release : 1952
Category : Harmonic analysis
ISBN : UVA:X001468995

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The Theory of Potential and Spherical Harmonics by Wolfgang J. Sternberg,Turner Linn Smith Pdf

Author : Avery James Emil,Avery John Scales
Publisher : World Scientific
Page : 300 pages
File Size : 49,5 Mb
Release : 2017-11-27
Category : Science
ISBN : 9789813229310

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Hyperspherical Harmonics And Their Physical Applications by Avery James Emil,Avery John Scales Pdf

Hyperspherical harmonics are extremely useful in nuclear physics and reactive scattering theory. However, their use has been confined to specialists with very strong backgrounds in mathematics. This book aims to change the theory of hyperspherical harmonics from an esoteric field, mastered by specialists, into an easily-used tool with a place in the working kit of all theoretical physicists, theoretical chemists and mathematicians. The theory presented here is accessible without the knowledge of Lie-groups and representation theory, and can be understood with an ordinary knowledge of calculus. The book is accompanied by programs and exercises designed for teaching and practical use. Contents: PrefaceHarmonic FunctionsGeneralized Angular MomentumGegenbauer PolynomialsFourier Transforms in d DimensionsFock's Treatment of Hydrogenlike Atoms and Its GeneralizationD-Dimensional Hydrogenlike Orbitals in Direct SpaceGeneralized SturmiansChoosing Appropriate Hyperspherical RepresentationsMolecular Integrals from Hyperspherical HarmonicsLagrangians for Particles and FieldsCoordinate Transformations for N BodiesSome Illustrative ExamplesAppendices: The D-Dimensional Harmonic OscillatorMolecular Integrals for Slatertype OrbitalsBibliographyIndex Readership: Scientists and researchers in theoretical physics, theoretical chemistry, and mathematics. Keywords: Harmonic Functions;Reactive Scattering Theory; Nuclear Physics;Gegenbauer Polynomials;Generalized Sturmians;Slatertype OrbitalsReview: Key Features: Exercises are included at the end of each chapterThe e-version of the exercises and solutions can be found in the supplementary tab

Author : Thomas Murray MacRobert
Publisher : Unknown
Page : 400 pages
File Size : 42,7 Mb
Release : 1947
Category : Functions
ISBN : UOM:39015000982663

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Spherical Harmonics by Thomas Murray MacRobert Pdf