Download or read book Harmonic Analysis of Spherical Functions on Real Reductive Groups written by Ramesh Gangolli and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 379 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 Spherical Functions of Mathematical Geosciences written by Willi Freeden and published by Springer Nature. This book was released on 2022 with total page 729 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an enlarged second edition of a monograph published in the Springer AGEM2-Series, 2009. It presents, in a consistent and unified overview, a setup of the theory of spherical functions of mathematical (geo-)sciences. The content shows a twofold transition: First, the natural transition from scalar to vectorial and tensorial theory of spherical harmonics is given in a coordinate-free context, based on variants of the addition theorem, Funk-Hecke formulas, and Helmholtz as well as Hardy-Hodge decompositions. Second, the canonical transition from spherical harmonics via zonal (kernel) functions to the Dirac kernel is given in close orientation to an uncertainty principle classifying the space/frequency (momentum) behavior of the functions for purposes of data analysis and (geo-)application. The whole palette of spherical functions is collected in a well-structured form for modeling and simulating the phenomena and processes occurring in the Earth's system. The result is a work which, while reflecting the present state of knowledge in a time-related manner, claims to be of largely timeless significance in (geo-)mathematical research and teaching.
Download or read book Spherical Functions of Mathematical Geosciences written by Willi Freeden and published by Springer Science & Business Media. This book was released on 2008-12-14 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the Geomathematics Group, TU Kaiserslautern, has worked to set up a theory of spherical functions of mathematical physics. This book is a collection of all the material that group generated during the process.
Download or read book Modern Spherical Functions written by Masaru Takeuchi and published by American Mathematical Soc.. This book was released on 1994 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an exposition of spherical functions on compact symmetric spaces, from the viewpoint of Cartan-Selberg. Representation theory, invariant differential operators, and invariant integral operators play an important role in the exposition. The author treats compact symmetric pairs, spherical representations for compact symmetric pairs, the fundamental groups of compact symmetric spaces, and the radial part of an invariant differential operator. Also explored are the classical results for spheres and complex projective spaces and the relation between spherical functions and harmonic polynomials. This book is suitable as a graduate textbook.
Download or read book Spherical Radial Basis Functions Theory and Applications written by Simon Hubbert and published by Springer. This book was released on 2015-05-13 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first to be devoted to the theory and applications of spherical (radial) basis functions (SBFs), which is rapidly emerging as one of the most promising techniques for solving problems where approximations are needed on the surface of a sphere. The aim of the book is to provide enough theoretical and practical details for the reader to be able to implement the SBF methods to solve real world problems. The authors stress the close connection between the theory of SBFs and that of the more well-known family of radial basis functions (RBFs), which are well-established tools for solving approximation theory problems on more general domains. The unique solvability of the SBF interpolation method for data fitting problems is established and an in-depth investigation of its accuracy is provided. Two chapters are devoted to partial differential equations (PDEs). One deals with the practical implementation of an SBF-based solution to an elliptic PDE and another which describes an SBF approach for solving a parabolic time-dependent PDE, complete with error analysis. The theory developed is illuminated with numerical experiments throughout. Spherical Radial Basis Functions, Theory and Applications will be of interest to graduate students and researchers in mathematics and related fields such as the geophysical sciences and statistics.
Download or read book Harmonic Analysis on Semi Simple Lie Groups II written by Garth Warner and published by Springer. This book was released on 1972-11-23 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Tables and Formulae for the Spherical Functions Pm 1 2 i t Z written by M. I. Zhurina and published by Elsevier. This book was released on 2014-07-14 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tables and Formulae for the Spherical Functions Pm – 1⁄2 + i t (Z)
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 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 The Augmented Spherical Wave Method written by Volker Eyert and published by Springer. This book was released on 2012-12-14 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Augmented Spherical Wave (ASW) method is one of the most powerful approaches to handle the requirements of finite basis sets in DFT calculations. It is particularly suited for the calculation of the electronic, magnetic, and optical properties of solid-state materials. Recent developments allow application, in addition, to the elastic properties and phonon spectra. Due to the localized nature of the ASW basis set these properties can be easily interpreted in terms of atomic-like orbitals. The book addresses all those who want to learn about methods for electronic structure calculations and the ASW method in particular. This new edition has been thoroughly revised and extended. In particular, a chapter on the new, both very efficient and accurate spherical-wave based full potential ASW method has been added.
Download or read book Fundamentals of Spherical Array Processing written by Boaz Rafaely and published by Springer. This book was released on 2018-09-27 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the theory and practice of spherical microphone arrays, and was written for graduate students, researchers and engineers who work with spherical microphone arrays in a wide range of applications. The new edition includes additions and modifications, and references supplementary Matlab code to provide the reader with a straightforward start for own implementations. The book is also accompanied by a Matlab manual, which explains how to implement the examples and simulations presented in the book. The first two chapters provide the reader with the necessary mathematical and physical background, including an introduction to the spherical Fourier transform and the formulation of plane-wave sound fields in the spherical harmonic domain. In turn, the third chapter covers the theory of spatial sampling, employed when selecting the positions of microphones to sample sound pressure functions in space. Subsequent chapters highlight various spherical array configurations, including the popular rigid-sphere-based configuration. Beamforming (spatial filtering) in the spherical harmonics domain, including axis-symmetric beamforming, and the performance measures of directivity index and white noise gain are introduced, and a range of optimal beamformers for spherical arrays, including those that achieve maximum directivity and maximum robustness are developed, along with the Dolph–Chebyshev beamformer. The final chapter discusses more advanced beamformers, such as MVDR (minimum variance distortionless response) and LCMV (linearly constrained minimum variance) types, which are tailored to the measured sound field. Mathworks kindly distributes the Matlab sources for this book on https://www.mathworks.com/matlabcentral/fileexchange/68655-fundamentals-of-spherical-array-processing.
Download or read book Spherical Sampling written by Willi Freeden and published by Birkhäuser. This book was released on 2018-05-03 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents, in a consistent and unified overview, results and developments in the field of today ́s spherical sampling, particularly arising in mathematical geosciences. Although the book often refers to original contributions, the authors made them accessible to (graduate) students and scientists not only from mathematics but also from geosciences and geoengineering. Building a library of topics in spherical sampling theory it shows how advances in this theory lead to new discoveries in mathematical, geodetic, geophysical as well as other scientific branches like neuro-medicine. A must-to-read for everybody working in the area of spherical sampling.
Download or read book Electromagnetic Fields Excited in Volumes with Spherical Boundaries written by Yuriy M. Penkin and published by Springer. This book was released on 2018-08-22 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the problem of electromagnetic wave excitation in spatial regions with spherical boundaries and the accurate mathematical modeling based on numerical and analytical methods to significantly reduce the time required for developing new antenna devices. It particularly focuses on elements and systems on mobile objects of complex shape that are made of new technological materials. The experimental development of such devices and systems is an extremely time-consuming, lengthy, and expensive process. The book is intended for senior and postgraduate students and researchers working in the fields of radiophysics, radio engineering and antenna design. The authors assume that readers understand the basics of vector and tensor analysis, as well as the general theory of electrodynamics. The original results presented can be directly used in the development of spherical antennas and antenna systems for the mobile objects. The book addresses problems concerning the construction of Green’s functions for Hertz potentials in electrodynamic volumes with spherical boundaries, and solves these clearly and concisely. It also uses specific examples to analyze areas where the results could potentially be applied. The book covers the following topics: · excitation of electromagnetic fields in coordinate electrodynamic volumes; · Green’s functions for spherical resonators; · Green’s functions for infinite space outside of spherical scatterers; · electromagnetic fields of dipole radiators on spherical scatterers; · electromagnetic fields of thin radial impedance vibrators on perfectly conducting spheres; · electrodynamic characteristics of narrow slots in spherical surfaces; · multi-element and combined vibrator-slot radiators on spherical surfaces.
Download or read book New Tables of Mie Scatteirng Functions for Spherical Particles written by Air Force Cambridge Research Laboratories (U.S.). Geophysics Research Directorate and published by . This book was released on 1956 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Applications of Fourier Series and Spherical Harmonics written by H. Groemer and published by Cambridge University Press. This book was released on 1996-09-13 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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:
