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Spherical Harmonics and Approximations on the Unit Sphere An Introduction

Spherical Harmonics and Approximations on the Unit Sphere  An Introduction Author Kendall Atkinson
ISBN-10 9783642259838
Release 2012-02-17
Pages 244
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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 and Harmonic Analysis on Spheres and Balls

Approximation Theory and Harmonic Analysis on Spheres and Balls Author Feng Dai
ISBN-10 9781461466604
Release 2013-04-17
Pages 440
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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.



Introduction to Radon Transforms

Introduction to Radon Transforms Author
ISBN-10 9780521854597
Release
Pages
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Introduction to Radon Transforms has been writing in one form or another for most of life. You can find so many inspiration from Introduction to Radon Transforms also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Introduction to Radon Transforms book for free.



Approximation Theory XIV San Antonio 2013

Approximation Theory XIV  San Antonio 2013 Author Gregory E. Fasshauer
ISBN-10 9783319064048
Release 2014-06-02
Pages 395
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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.



Spherical Radial Basis Functions Theory and Applications

Spherical Radial Basis Functions  Theory and Applications Author Simon Hubbert
ISBN-10 9783319179391
Release 2015-05-13
Pages 143
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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.



Spectral Analysis on Graph like Spaces

Spectral Analysis on Graph like Spaces Author Olaf Post
ISBN-10 9783642238390
Release 2012-01-06
Pages 431
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Small-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analysis. In this monograph, we analyse Laplace-like operators on thin tubular structures ("graph-like spaces''), and their natural limits on metric graphs. In particular, we explore norm resolvent convergence, convergence of the spectra and resonances. Since the underlying spaces in the thin radius limit change, and become singular in the limit, we develop new tools such as norm convergence of operators acting in different Hilbert spaces, an extension of the concept of boundary triples to partial differential operators, and an abstract definition of resonances via boundary triples. These tools are formulated in an abstract framework, independent of the original problem of graph-like spaces, so that they can be applied in many other situations where the spaces are perturbed.



Harmonic analysis and approximation on the unit sphere

Harmonic analysis and approximation on the unit sphere Author Kunyang Wang
ISBN-10 7030083660
Release 2000-07
Pages 300
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Spherical Harmonics

Spherical Harmonics Author Claus Müller
ISBN-10 9783540371748
Release 2006-11-14
Pages 52
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Spherical Harmonics has been writing in one form or another for most of life. You can find so many inspiration from Spherical Harmonics also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Spherical Harmonics book for free.



Tutorials on Multiresolution in Geometric Modelling

Tutorials on Multiresolution in Geometric Modelling Author Armin Iske
ISBN-10 3540436391
Release 2002-06-12
Pages 421
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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/.



Theoretical Numerical Analysis

Theoretical Numerical Analysis Author Kendall Atkinson
ISBN-10 9781441904584
Release 2009-06-12
Pages 625
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This textbook prepares graduate students for research in numerical analysis/computational mathematics by giving to them a mathematical framework embedded in functional analysis and focused on numerical analysis. This helps the student to move rapidly into a research program. The text covers basic results of functional analysis, approximation theory, Fourier analysis and wavelets, iteration methods for nonlinear equations, finite difference methods, Sobolev spaces and weak formulations of boundary value problems, finite element methods, elliptic variational inequalities and their numerical solution, numerical methods for solving integral equations of the second kind, and boundary integral equations for planar regions. The presentation of each topic is meant to be an introduction with certain degree of depth. Comprehensive references on a particular topic are listed at the end of each chapter for further reading and study. Because of the relevance in solving real world problems, multivariable polynomials are playing an ever more important role in research and applications. In this third editon, a new chapter on this topic has been included and some major changes are made on two chapters from the previous edition. In addition, there are numerous minor changes throughout the entire text and new exercises are added. Review of earlier edition: "...the book is clearly written, quite pleasant to read, and contains a lot of important material; and the authors have done an excellent job at balancing theoretical developments, interesting examples and exercises, numerical experiments, and bibliographical references." R. Glowinski, SIAM Review, 2003



Mathematical Reviews

Mathematical Reviews Author
ISBN-10 UVA:X006195258
Release 2005
Pages
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Mathematical Reviews has been writing in one form or another for most of life. You can find so many inspiration from Mathematical Reviews also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Mathematical Reviews book for free.



Mathematical Methods for Protein Structure Analysis and Design

Mathematical Methods for Protein Structure Analysis and Design Author Concettina Guerra
ISBN-10 9783540401049
Release 2003-06-25
Pages 157
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The papers collected in this volume reproduce contributions by leading sch- arstoaninternationalschoolandworkshopwhichwasorganizedandheldwith thegoaloftakinga snapshotofadiscipline undertumultuous growth. Indeed, the area of protein folding, docking and alignment is developing in response to needs for a mix of heterogeneous expertise spanning biology, chemistry, mathematics, computer science, and statistics, among others. Some of the problems encountered in this area are not only important for the scienti?c challenges they pose, but also for the opportunities they disclose intermsofmedicalandindustrialexploitation. Atypicalexampleiso?eredby protein-drug interaction (docking), a problem posing daunting computational problems at the crossroads of geometry, physics and chemistry, and, at the same time, a problem with unimaginable implications for the pharmacopoeia of the future. The schoolfocused on problems posed by the study of the mechanisms - hind protein folding, and explored di?erent ways of attacking these problems under objective evaluations of the methods. Together with a relatively small core of consolidated knowledge and tools, important re?ections were brought to this e?ort by studies in a multitude of directions and approaches. It is obviously impossible to predict which, if any, among these techniques will prove completely successful, but it is precisely the implicit dialectic among them that best conveys the current ?avor of the ?eld. Such unique diversity and richness inspired the format of the meeting, and also explains the slight departure of the present volume from the typical format in this series: the exposition of the current sediment is complemented here by a selection of quali?ed specialized contributions.



The Ricci Flow in Riemannian Geometry

The Ricci Flow in Riemannian Geometry Author Ben Andrews
ISBN-10 9783642162855
Release 2010-11-25
Pages 296
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Focusing on Hamilton's Ricci flow, this volume begins with a detailed discussion of the required aspects of differential geometry. The discussion also includes existence and regularity theory, compactness theorems for Riemannian manifolds, and much more.



Harmonic Function Theory

Harmonic Function Theory Author Sheldon Axler
ISBN-10 9781475781373
Release 2013-11-11
Pages 264
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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.



Chebyshev and Fourier Spectral Methods

Chebyshev and Fourier Spectral Methods Author John P. Boyd
ISBN-10 9780486141923
Release 2013-06-05
Pages 688
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Completely revised text applies spectral methods to boundary value, eigenvalue, and time-dependent problems, but also covers cardinal functions, matrix-solving methods, coordinate transformations, much more. Includes 7 appendices and over 160 text figures.



Lectures on Classical Differential Geometry

Lectures on Classical Differential Geometry Author Dirk Jan Struik
ISBN-10 0486656098
Release 1961
Pages 232
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Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student. Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Dr. Struik has enhanced the treatment with copious historical, biographical, and bibliographical references that place the theory in context and encourage the student to consult original sources and discover additional important ideas there. For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thought-provoking text — ideal for classroom use, but also perfectly suited for self-study. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry.



The Mathematics of Diffusion

The Mathematics of Diffusion Author John Crank
ISBN-10 0198534116
Release 1979
Pages 414
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Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.