Download or read book Mechanization of Spherical Harmonic Analysis written by B. R. Leaton and published by . This book was released on 1967 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spherical Harmonic Analysis written by Paul F. Fougère and published by . This book was released on 1965 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 the theory of spherical and ellipsoidal harmonics written by E. W. Hobson and published by CUP Archive. This book was released on with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Example of the Use of Spherical Harmonic Analysis written by Herbert Hall Turner and published by . This book was released on 1912 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 of Spherical Functions on Real Reductive Groups written by R. A. Gangolli and published by Springer. This book was released on 1988 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis on Symmetric spaces, or more generally, on homogeneous spaces of semisimple Lie groups, is a subject that has undergone a vigorous development in recent years, and has become a central part of contemporary mathematics. This is only to be expected, since homogeneous spaces and group representations arise naturally in diverse contexts ranging from Number theory and Geometry to Particle Physics and Polymer Chemistry. Its explosive growth sometimes makes it difficult to realize that it is actually relatively young as mathematical theories go. The early ideas in the subject (as is the case with many others) go back to Elie Cart an and Hermann Weyl who studied the compact symmetric spaces in the 1930's. However its full development did not begin until the 1950's when Gel'fand and Harish Chandra dared to dream of a theory of representations that included all semisimple Lie groups. Harish-Chandra's theory of spherical functions was essentially complete in the late 1950's, and was to prove to be the forerunner of his monumental work on harmonic analysis on reductive groups that has inspired a whole generation of mathematicians. It is the harmonic analysis of spherical functions on symmetric spaces, that is at the focus of this book. The fundamental questions of harmonic analysis on symmetric spaces involve an interplay of the geometric, analytical, and algebraic aspects of these spaces. They have therefore attracted a great deal of attention, and there have been many excellent expositions of the themes that are characteristic of this subject.
Download or read book Harmonic Analysis on Real Reductive Groups written by V.S. Varadarajan and published by Springer. This book was released on 2006-11-14 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 A Panorama of Harmonic Analysis written by Steven G. Krantz and published by American Mathematical Soc.. This book was released on 2019-07-03 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Panorama of Harmonic Analysis treats the subject of harmonic analysis, from its earliest beginnings to the latest research. Following both an historical and a conceptual genesis, the book discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space. The climax of the book is a consideration of the earlier ideas from the point of view of spaces of homogeneous type. The book culminates with a discussion of wavelets-one of the newest ideas in the subject. A Panorama of Harmonic Analysis is intended for graduate students, advanced undergraduates, mathematicians, and anyone wanting to get a quick overview of the subject of cummutative harmonic analysis. Applications are to mathematical physics, engineering and other parts of hard science. Required background is calculus, set theory, integration theory, and the theory of sequences and series.
Download or read book The Theory of Spherical and Ellipsoidal Harmonics written by Ernest William Hobson and published by . This book was released on 1965 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Equilvalence of the Spherical Harmonics Method and the Discrete Ordinate Method Using Gauss Quadrature for the Boltzman Equation written by Robert Gast and published by . This book was released on 1958 with total page 44 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 Numerical Methods for Harmonic Analysis on the Sphere written by Oscar L. Colombo and published by . This book was released on 1981 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report presents some numerical methods for estimating spherical harmonic coefficients from data sampled on the sphere. The data may be given in the form of area means or of point values, and it may be free from errors or affected by measurement 'noise'. The case discussed to greatest length is that of complete, global data sets on regular grids (i.e., lines of latitude and longitude, the latter, at least, separated by constant interval); the case where data are sparsely and irregularly distributed is also considered in some detail. The first section presents some basic properties of spherical harmonics, stressing their relationship to two-dimensional Fourier series. Algorithms for the evaluation of the harmonic coefficients by numerical quadratures are given here, and it is shown that the number of operations is the order of N cubed for equal angular grids, where N is the number of lines of latitude, or 'Nyquist frequency', of the grid. The second section introduces a quadratic measure for the error in the estimation of the coefficients by linear techniques. This is the error measure of least squares collocation, which is a method that can be used for harmonic analysis. Efficient algorithms for implementing collocation on the whole sphere are described. a formal relationship between collocation and least squares adjustment is used to obtain an alternative form of the collocation algorithm that is likely to be stable with dense data sets and, with a minor modification, can be used to implement least squares adjustment as well. The basic principle is that for regular grids the variance-convariance matrix of the data consists of Toeplitz-circulant blocks, so it can be both set up and inverted very efficiently.
Download or read book Harmonic Analysis on Symmetric Spaces and Applications I written by Audrey Terras and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its beginnings with Fourier (and as far back as the Babylonian astron omers), harmonic analysis has been developed with the goal of unraveling the mysteries of the physical world of quasars, brain tumors, and so forth, as well as the mysteries of the nonphysical, but no less concrete, world of prime numbers, diophantine equations, and zeta functions. Quoting Courant and Hilbert, in the preface to the first German edition of Methods of Mathematical Physics: "Recent trends and fashions have, however, weakened the connection between mathematics and physics. " Such trends are still in evidence, harmful though they may be. My main motivation in writing these notes has been a desire to counteract this tendency towards specialization and describe appli cations of harmonic analysis in such diverse areas as number theory (which happens to be my specialty), statistics, medicine, geophysics, and quantum physics. I remember being quite surprised to learn that the subject is useful. My graduate eduation was that of the 1960s. The standard mathematics graduate course proceeded from Definition 1. 1. 1 to Corollary 14. 5. 59, with no room in between for applications, motivation, history, or references to related work. My aim has been to write a set of notes for a very different sort of course.
Download or read book Spherical Harmonic Analysis I written by Paul F. Fougere and published by . This book was released on 1963 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new method for performing a spherical harmonic analysis, using only observed components of the earth's magnetic field, is presented. Essential features of the method involve the use of (1) multidimensional vector spaces to exhibit clearllrand to make use of the coupling amound the X, Y, and Z expansions and to simplify the logic, (2) the Gram-SSHMIDT ORTHOGONALIZATION PROCESS TO SIMPLIFY THE SOLUTION OF THE NORMAL EQUATIONS OF LEAST SQUARES AND, MORE IMPORTANT, TO PROVIDE A SYSTEM OF ORTHOGONAL FUNCTIONS WITH THEIR MANY USEFUL PROPERTIES; AND (3) the variance ration test appaied to each orthogonal function in such a way that the significant functions are used in the final approximation and the insig cificant ones are used to estimate error. The method is verified by applying to to two indepen dent sets of data, both derived by evaluating a given set of Gaussian coefficients. That the method works in the error-free case is proved conclusively by the remarkable agreement between input and output coefficients for both sets of data. (Author).
