Spherical Harmonics and Approximations on the Unit Sphere An Introduction

Author: Kendall Atkinson
Publisher: Springer Science & Business Media
ISBN: 3642259839
Format: PDF, ePub
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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.

Approximation Theory XIV San Antonio 2013

Author: Gregory E. Fasshauer
Publisher: Springer
ISBN: 3319064045
Format: PDF, ePub, Mobi
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These proceedings were prepared in connection with the 14th International Conference on Approximation Theory, which was held April 7-10, 2013 in San Antonio, Texas. The conference was the fourteenth in a series of meetings in Approximation Theory held at various locations in the United States. The included invited and contributed papers cover diverse areas of approximation theory with a special emphasis on the most current and active areas such as compressed sensing, isogeometric analysis, anisotropic spaces, radial basis functions and splines. Classical and abstract approximation is also included. The book will be of interest to mathematicians, engineers\ and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis and related application areas.

Approximation Theory and Harmonic Analysis on Spheres and Balls

Author: Feng Dai
Publisher: Springer Science & Business Media
ISBN: 1461466601
Format: PDF
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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.

Spherical Radial Basis Functions Theory and Applications

Author: Simon Hubbert
Publisher: Springer
ISBN: 331917939X
Format: PDF, Docs
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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.

Geometrie und Billard

Author: Serge Tabachnikov
Publisher: Springer-Verlag
ISBN: 3642319254
Format: PDF, ePub
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Wie bewegt sich ein Massenpunkt in einem Gebiet, an dessen Rand er elastisch zurückprallt? Welchen Weg nimmt ein Lichtstrahl in einem Gebiet mit ideal reflektierenden Rändern? Anhand dieser und ähnlicher Fragen stellt das vorliegende Buch Zusammenhänge zwischen Billard und Differentialgeometrie, klassischer Mechanik sowie geometrischer Optik her. Dabei beschäftigt sich das Buch unter anderem mit dem Variationsprinzip beim mathematischen Billard, der symplektischen Geometrie von Lichtstrahlen, der Existenz oder Nichtexistenz von Kaustiken, periodischen Billardtrajektorien und dem Mechanismus für Chaos bei der Billarddynamik. Ergänzend wartet dieses Buch mit einer beachtlichen Anzahl von Exkursen auf, die sich verwandten Themen widmen, darunter der Vierfarbensatz, die mathematisch-physikalische Beschreibung von Regenbögen, der poincaresche Wiederkehrsatz, Hilberts viertes Problem oder der Schließungssatz von Poncelet.​

Grundkurs Theoretische Physik 3

Author: Wolfgang Nolting
Publisher: Springer-Verlag
ISBN: 3642379052
Format: PDF
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Der Grundkurs Theoretische Physik deckt in sieben Bänden alle für Bachelor-, Master- oder Diplom-Studiengänge maßgeblichen Gebiete ab. Jeder Band vermittelt gut durchdacht das im jeweiligen Semester benötigte theoretisch-physikalische Wissen. Der 3. Band behandelt die Elektrodynamik in ihrer induktiven Formulierung. Mathematische Inhalte (Vektoranalysis) werden immer dann in den Text eingeschoben, wenn sie für das weitere Verständnis unverzichtbar sind. Der Band enthält in der 10. Auflage mehr als 200 Abbildungen, neue Übungsaufgaben und Lösungen und ist im Ganzen überarbeitet und aktualisiert worden.

Tutorials on Multiresolution in Geometric Modelling

Author: Armin Iske
Publisher: Springer Science & Business Media
ISBN: 9783540436393
Format: PDF, Kindle
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This is the only textbook available on multiresolution methods in geometric modeling, a central topic in visualization, which is of great importance for industrial applications. Written in tutorial form, the book is introductory in character, and includes supporting exercises. Other supplementary material and software can be downloaded from the website www.ma.tum.de/primus 2001/.