Analysis Of Spherical Symmetries In Euclidean Spaces

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Analysis of Spherical Symmetries in Euclidean Spaces

Author : Claus Müller
Publisher : Springer Science & Business Media
ISBN 13 : 1461205816
Total Pages : 227 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Analysis of Spherical Symmetries in Euclidean Spaces by : Claus Müller

Download or read book Analysis of Spherical Symmetries in Euclidean Spaces written by Claus Müller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book offers a new and direct approach to the theories of special functions with emphasis on spherical symmetry in Euclidean spaces of arbitrary dimensions. Based on many years of lecturing to mathematicians, physicists and engineers in scientific research institutions in Europe and the USA, the author uses elementary concepts to present the spherical harmonics in a theory of invariants of the orthogonal group. One of the highlights is the extension of the classical results of the spherical harmonics into the complex - particularly important for the complexification of the Funk-Hecke formula which successfully leads to new integrals for Bessel- and Hankel functions with many applications of Fourier integrals and Radon transforms. Numerous exercises stimulate mathematical ingenuity and bridge the gap between well-known elementary results and their appearance in the new formations.

Analysis of Spherical Symmetries in Euclidean Spaces

Author : Claus Muller
Publisher :
ISBN 13 : 9781461205821
Total Pages : 240 pages
Book Rating : 4.2/5 (58 download)

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Book Synopsis Analysis of Spherical Symmetries in Euclidean Spaces by : Claus Muller

Download or read book Analysis of Spherical Symmetries in Euclidean Spaces written by Claus Muller and published by . This book was released on 1997-11-01 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane

Author : Audrey Terras
Publisher : Springer Science & Business Media
ISBN 13 : 146147972X
Total Pages : 430 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane by : Audrey Terras

Download or read book Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane written by Audrey Terras and published by Springer Science & Business Media. This book was released on 2013-09-12 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincaré upper half plane. This book is intended for beginning graduate students in mathematics or researchers in physics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, and engineering. Many corrections and updates have been incorporated in this new edition. Updates include discussions of P. Sarnak and others' work on quantum chaos, the work of T. Sunada, Marie-France Vignéras, Carolyn Gordon, and others on Mark Kac's question "Can you hear the shape of a drum?", A. Lubotzky, R. Phillips and P. Sarnak's examples of Ramanujan graphs, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summation formula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon transform, non-Euclidean geometry on the Poincaré upper half plane H or unit disc and applications to microwave engineering, fundamental domains in H for discrete groups Γ, tessellations of H from such discrete group actions, automorphic forms, and the Selberg trace formula and its applications in spectral theory as well as number theory.

Introduction to Fourier Analysis on Euclidean Spaces

Author : Elias M. Stein
Publisher : Princeton University Press
ISBN 13 : 9780691080789
Total Pages : 318 pages
Book Rating : 4.0/5 (87 download)

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Book Synopsis Introduction to Fourier Analysis on Euclidean Spaces by : Elias M. Stein

Download or read book Introduction to Fourier Analysis on Euclidean Spaces written by Elias M. Stein and published by Princeton University Press. This book was released on 1971-11-21 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.

Spherical Harmonics and Approximations on the Unit Sphere: An Introduction

Author : Kendall Atkinson
Publisher : Springer Science & Business Media
ISBN 13 : 3642259820
Total Pages : 253 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Spherical Harmonics and Approximations on the Unit Sphere: An Introduction by : Kendall Atkinson

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.

Robust Cluster Analysis and Variable Selection

Author : Gunter Ritter
Publisher : CRC Press
ISBN 13 : 1439857970
Total Pages : 389 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Robust Cluster Analysis and Variable Selection by : Gunter Ritter

Download or read book Robust Cluster Analysis and Variable Selection written by Gunter Ritter and published by CRC Press. This book was released on 2014-09-02 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clustering remains a vibrant area of research in statistics. Although there are many books on this topic, there are relatively few that are well founded in the theoretical aspects. This book presents an overview of the theory and applications of probabilistic clustering and variable selection, synthesizing the key research results of the last 50 years. It includes all the important theoretical details, and covers the probabilistic models and inference, robustness issues, optimization algorithms, validation techniques and variable selection methods. The book illustrates the different methods with simulated data and applies them to real-world data sets that can be easily downloaded from the web.

Scale Space and Variational Methods in Computer Vision

Author : Xue-Cheng Tai
Publisher : Springer Science & Business Media
ISBN 13 : 3642022553
Total Pages : 882 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Scale Space and Variational Methods in Computer Vision by : Xue-Cheng Tai

Download or read book Scale Space and Variational Methods in Computer Vision written by Xue-Cheng Tai and published by Springer Science & Business Media. This book was released on 2009-05-25 with total page 882 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second International Conference on Scale Space Methods and Variational Methods in Computer Vision, SSVM 2009, emanated from the joint edition of the 5th International Workshop on Variational, Geometric and Level Set Methods in Computer Vision, VLSM 2009 and the 7th International Conference on Scale Space and PDE Methods in Computer Vision, Scale-Space 2009, held in Voss, Norway in June 2009. The 71 revised full papers presented were carefully reviewed and selected numerous submissions. The papers are organized in topical sections on segmentation and detection; image enhancement and reconstruction; motion analysis, optical flow, registration and tracking; surfaces and shapes; scale space and feature extraction.

Emerging Trends in Knowledge Discovery and Data Mining

Author : Takashi Washio
Publisher : Springer
ISBN 13 : 364236778X
Total Pages : 168 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Emerging Trends in Knowledge Discovery and Data Mining by : Takashi Washio

Download or read book Emerging Trends in Knowledge Discovery and Data Mining written by Takashi Washio and published by Springer. This book was released on 2013-02-13 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed proceedings of the PAKDD 2012 International Workshops: Third Workshop on Data Mining for Healthcare Management (DMHM 2012), First Workshop on Geospatial Information and Documents (GeoDoc 2012), First Workshop on Multi-view data, High-dimensionality, External Knowledge: Striving for a Unified Approach to Clustering (3Clust 2012), and the Second Doctoral Symposium on Data Mining (DSDM 2012); held in conjunction with the 16th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD 2012), in Kuala Lumpur, Malaysia, May/June 2012. The 12 revised papers presented were carefully reviewed and selected from numerous submissions. DMHM 2012 aimed at providing a common platform for the discussion of challenging issues and potential techniques in this emerging field of data mining for health care management; 3Clust 2012 focused on solving emerging problems such as clustering ensembles, semi-supervised clustering, subspace/projective clustering, co-clustering, and multi-view clustering; GeoDoc 2012 highlighted the formalization of geospatial concepts and relationships with a focus on the extraction of geospatial relations in free text datasets to offer to the database community a unified framework for geodata discovery; and DSDM 2012 provided the opportunity for Ph.D. students and junior researchers to discuss their work on data mining foundations, techniques and applications.

Offbeat Integral Geometry on Symmetric Spaces

Author : Valery V. Volchkov
Publisher : Springer Science & Business Media
ISBN 13 : 3034805721
Total Pages : 596 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Offbeat Integral Geometry on Symmetric Spaces by : Valery V. Volchkov

Download or read book Offbeat Integral Geometry on Symmetric Spaces written by Valery V. Volchkov and published by Springer Science & Business Media. This book was released on 2013-01-30 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book demonstrates the development of integral geometry on domains of homogeneous spaces since 1990. It covers a wide range of topics, including analysis on multidimensional Euclidean domains and Riemannian symmetric spaces of arbitrary ranks as well as recent work on phase space and the Heisenberg group. The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern versions of the Pompeiu problem, and explicit reconstruction formulae in problems of integral geometry. These results are intriguing and useful in various fields of contemporary mathematics. The proofs given are “minimal” in the sense that they involve only those concepts and facts which are indispensable for the essence of the subject. Each chapter provides a historical perspective on the results presented and includes many interesting open problems. Readers will find this book relevant to harmonic analysis on homogeneous spaces, invariant spaces theory, integral transforms on symmetric spaces and the Heisenberg group, integral equations, special functions, and transmutation operators theory.

Harmonic Analysis in Euclidean Spaces, Part 2

Author : Guido Weiss
Publisher : American Mathematical Soc.
ISBN 13 : 0821814389
Total Pages : 448 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Harmonic Analysis in Euclidean Spaces, Part 2 by : Guido Weiss

Download or read book Harmonic Analysis in Euclidean Spaces, Part 2 written by Guido Weiss and published by American Mathematical Soc.. This book was released on 1979 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains sections on Several complex variables, Pseudo differential operators and partial differential equations, Harmonic analysis in other settings: probability, martingales, local fields, and Lie groups and functional analysis.

Mathematical Problems in Image Processing

Author : Gilles Aubert
Publisher : Springer Science & Business Media
ISBN 13 : 0387445889
Total Pages : 400 pages
Book Rating : 4.3/5 (874 download)

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Book Synopsis Mathematical Problems in Image Processing by : Gilles Aubert

Download or read book Mathematical Problems in Image Processing written by Gilles Aubert and published by Springer Science & Business Media. This book was released on 2006-11-30 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The updated 2nd edition of this book presents a variety of image analysis applications, reviews their precise mathematics and shows how to discretize them. For the mathematical community, the book shows the contribution of mathematics to this domain, and highlights unsolved theoretical questions. For the computer vision community, it presents a clear, self-contained and global overview of the mathematics involved in image procesing problems. The second edition offers a review of progress in image processing applications covered by the PDE framework, and updates the existing material. The book also provides programming tools for creating simulations with minimal effort.

Stability and Wave Motion in Porous Media

Author : Brian Straughan
Publisher : Springer Science & Business Media
ISBN 13 : 0387765433
Total Pages : 445 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Stability and Wave Motion in Porous Media by : Brian Straughan

Download or read book Stability and Wave Motion in Porous Media written by Brian Straughan and published by Springer Science & Business Media. This book was released on 2008-12-10 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes several tractable theories for fluid flow in porous media. The important mathematical quations about structural stability and spatial decay are address. Thermal convection and stability of other flows in porous media are covered. A chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer. Nonlinear wave motion in porous media is analysed. In particular, waves in an elastic body with voids are investigated while acoustic waves in porous media are also analysed in some detail. A chapter is enclosed on efficient numerical methods for solving eigenvalue problems which occur in stability problems for flows in porous media. Brian Straughan is a professor at the Department of Mathemactical Sciences at Durham University, United Kingdom.

Elements of Applied Bifurcation Theory

Author : Yuri Kuznetsov
Publisher : Springer Science & Business Media
ISBN 13 : 1475739788
Total Pages : 648 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Elements of Applied Bifurcation Theory by : Yuri Kuznetsov

Download or read book Elements of Applied Bifurcation Theory written by Yuri Kuznetsov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.

Bifurcation Theory

Author : Hansjörg Kielhöfer
Publisher : Springer Science & Business Media
ISBN 13 : 0387216332
Total Pages : 355 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Bifurcation Theory by : Hansjörg Kielhöfer

Download or read book Bifurcation Theory written by Hansjörg Kielhöfer and published by Springer Science & Business Media. This book was released on 2006-04-10 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations.

The Energy Method, Stability, and Nonlinear Convection

Author : brian straughan
Publisher : Springer Science & Business Media
ISBN 13 : 9780387004532
Total Pages : 470 pages
Book Rating : 4.0/5 (45 download)

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Book Synopsis The Energy Method, Stability, and Nonlinear Convection by : brian straughan

Download or read book The Energy Method, Stability, and Nonlinear Convection written by brian straughan and published by Springer Science & Business Media. This book was released on 2003-10-01 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Six new chapters (14-19) deal with topics of current interest: multi-component convection diffusion, convection in a compressible fluid, convenction with temperature dependent viscosity and thermal conductivity, penetrative convection, nonlinear stability in ocean circulation models, and numerical solution of eigenvalue problems.

Hypersingular Integrals and Their Applications

Author : Stefan Samko
Publisher : CRC Press
ISBN 13 : 9780415272681
Total Pages : 382 pages
Book Rating : 4.2/5 (726 download)

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Book Synopsis Hypersingular Integrals and Their Applications by : Stefan Samko

Download or read book Hypersingular Integrals and Their Applications written by Stefan Samko and published by CRC Press. This book was released on 2001-10-25 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hypersingular integrals arise as constructions inverse to potential-type operators and are realized by the methods of regularization and finite differences. This volume develops these approaches in a comprehensive treatment of hypersingular integrals and their applications. The author is a renowned expert on the topic. He explains the basics before building more sophisticated ideas, and his discussions include a description of hypersingular integrals as they relate to functional spaces. Hypersingular Integrals and Their Applications also presents recent results and applications that will prove valuable to graduate students and researchers working in mathematical analysis.

Linear Operator Theory in Engineering and Science

Author : Arch W. Naylor
Publisher : Springer Science & Business Media
ISBN 13 : 9780387950013
Total Pages : 648 pages
Book Rating : 4.9/5 (5 download)

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Book Synopsis Linear Operator Theory in Engineering and Science by : Arch W. Naylor

Download or read book Linear Operator Theory in Engineering and Science written by Arch W. Naylor and published by Springer Science & Business Media. This book was released on 1982 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a unique introduction to the theory of linear operators on Hilbert space. The authors' goal is to present the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented. First published in 1971, Linear Operator in Engineering and Sciences has since proved to be a popular and very useful textbook.