Computation of Spherical Harmonics and Approximation by Spherical Harmonic Expansions PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Computation of Spherical Harmonics and Approximation by Spherical Harmonic Expansions PDF full book. Access full book title Computation of Spherical Harmonics and Approximation by Spherical Harmonic Expansions by W. Freeden. Download full books in PDF and EPUB format.
Author: W. Freeden
Publisher:
ISBN:
Category : Geodesy
Languages : en
Pages : 696
Get Book Here
Book Description
Author: W. Freeden
Publisher:
ISBN:
Category : Geodesy
Languages : en
Pages : 696
Get Book Here
Book Description
Author: Willi Freeden
Publisher:
ISBN:
Category : Gravity
Languages : en
Pages : 133
Get Book Here
Book Description
A technique is developed for generating spherical harmonics by exact computation (in integer mode) thereby circumventing any source of rounding errors. Essential results of the theory of spherical harmonics are recapitulated by intrinsic properties of the space of homogeneous harmonic polynomials. Exact computation of (maximal) linearly independent and orthonormal systems of spherical harmonics is explained using exclusively integer operations. The numerical efficiency is discussed. The development of exterior gravitational potential in a series of outer (spherical) harmonics is investigated. Some numerical examples are given for solving exterior Dirichlet's boundary-value problems by use of outer (spherical) harmonic expansions for not-necessarily spherical boundaries. Keywords: Homogeneous harmonic polynomials; Spherical harmonics; Exact computation in integer mode; Series expansion into spherical harmonics; Exterior dirichlet's problem.
Author: Kendall Atkinson
Publisher: Springer Science & Business Media
ISBN: 3642259820
Category : Mathematics
Languages : en
Pages : 253
Get Book Here
Book Description
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
Publisher: World Scientific
ISBN: 981459671X
Category : Mathematics
Languages : en
Pages : 156
Get Book Here
Book Description
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.
Author: W. Freeden
Publisher:
ISBN:
Category :
Languages : en
Pages : 133
Get Book Here
Book Description
Author: Wolfgang J. Sternberg
Publisher:
ISBN:
Category : Harmonic analysis
Languages : en
Pages : 332
Get Book Here
Book Description
Author: Claus Müller
Publisher: Springer
ISBN: 3540371745
Category : Mathematics
Languages : en
Pages : 50
Get Book Here
Book Description
Author: Feng Dai
Publisher: Springer Science & Business Media
ISBN: 1461466601
Category : Mathematics
Languages : en
Pages : 447
Get Book Here
Book Description
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: John S. Avery
Publisher: Springer Science & Business Media
ISBN: 9400923236
Category : Science
Languages : en
Pages : 265
Get Book Here
Book Description
where d 3 3)2 ( L x - -- i3x j3x j i i>j Thus the Gegenbauer polynomials play a role in the theory of hyper spherical harmonics which is analogous to the role played by Legendre polynomials in the familiar theory of 3-dimensional spherical harmonics; and when d = 3, the Gegenbauer polynomials reduce to Legendre polynomials. The familiar sum rule, in 'lrlhich a sum of spherical harmonics is expressed as a Legendre polynomial, also has a d-dimensional generalization, in which a sum of hyper spherical harmonics is expressed as a Gegenbauer polynomial (equation (3-27»: The hyper spherical harmonics which appear in this sum rule are eigenfunctions of the generalized angular monentum 2 operator A , chosen in such a way as to fulfil the orthonormality relation: VIe are all familiar with the fact that a plane wave can be expanded in terms of spherical Bessel functions and either Legendre polynomials or spherical harmonics in a 3-dimensional space. Similarly, one finds that a d-dimensional plane wave can be expanded in terms of HYPERSPHERICAL HARMONICS xii "hyperspherical Bessel functions" and either Gegenbauer polynomials or else hyperspherical harmonics (equations ( 4 - 27) and ( 4 - 30) ) : 00 ik·x e = (d-4)!!A~oiA(d+2A-2)j~(kr)C~(~k'~) 00 (d-2)!!I(0) 2: iAj~(kr) 2:Y~ (["2k)Y (["2) A A=O ). l). l)J where I(O) is the total solid angle. This expansion of a d-dimensional plane wave is useful when we wish to calculate Fourier transforms in a d-dimensional space.
Author: Kunyang Wang
Publisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 320
Get Book Here
Book Description
