Download or read book Computation of Spherical Harmonics and Approximation by Spherical Harmonic Expansions written by W. Freeden and published by . This book was released on 1985 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computation of Spherical Harmonics and Approximation by Spherical Harmonic Expansions written by Willi Freeden and published by . This book was released on 1985 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spherical Harmonics and Approximations on the Unit Sphere An Introduction written by Kendall Atkinson and published by Springer Science & Business Media. This book was released on 2012-02-17 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spherical Harmonics In P Dimensions written by Costas Efthimiou and published by World Scientific. This book was released on 2014-03-07 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Computation of Spherical Harminics and Approximation by Spherical Harmonic Expansions written by W. Freeden and published by . This book was released on 1985 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation Theory and Harmonic Analysis on Spheres and Balls written by Feng Dai and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Theory of Potential and Spherical Harmonics written by Wolfgang J. Sternberg and published by . This book was released on 1952 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Harmonic Function Theory written by Sheldon Axler and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to improve the text. A unique software package supplements the text for readers who wish to explore harmonic function theory on a computer.
Download or read book Spherical Harmonics written by Claus Müller and published by Springer. This book was released on 2006-11-14 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Harmonic Analysis and Approximation on the Unit Sphere written by Kunyang Wang and published by . This book was released on 2000 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hyperspherical Harmonics written by John S. Avery and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Applications of the Simplified Spherical Harmonics Equations in Spherical Geometry written by Ely M. Gelbard and published by . This book was released on 1962 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Geomathematics written by Amir Z. Averbuch and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Face Processing Advanced Modeling and Methods written by Wenyi Zhao and published by Elsevier. This book was released on 2011-07-28 with total page 755 pages. Available in PDF, EPUB and Kindle. Book excerpt: Major strides have been made in face processing in the last ten years due to the fast growing need for security in various locations around the globe. A human eye can discern the details of a specific face with relative ease. It is this level of detail that researchers are striving to create with ever evolving computer technologies that will become our perfect mechanical eyes. The difficulty that confronts researchers stems from turning a 3D object into a 2D image. That subject is covered in depth from several different perspectives in this volume. Face Processing: Advanced Modeling and Methods begins with a comprehensive introductory chapter for those who are new to the field. A compendium of articles follows that is divided into three sections. The first covers basic aspects of face processing from human to computer. The second deals with face modeling from computational and physiological points of view. The third tackles the advanced methods, which include illumination, pose, expression, and more. Editors Zhao and Chellappa have compiled a concise and necessary text for industrial research scientists, students, and professionals working in the area of image and signal processing. Contributions from over 35 leading experts in face detection, recognition and image processing Over 150 informative images with 16 images in FULL COLOR illustrate and offer insight into the most up-to-date advanced face processing methods and techniques Extensive detail makes this a need-to-own book for all involved with image and signal processing
Download or read book Chebyshev and Fourier Spectral Methods written by John P. Boyd and published by Courier Corporation. This book was released on 2001-12-03 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: Completely revised 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, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.
Download or read book An Elementary Treatise on Spherical Harmonics and Subjects Connected with Them written by Norman M. Ferrers and published by . This book was released on 1877 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spherical Harmonics written by Claus Muller and published by . This book was released on 2014-01-15 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
