Analysis of Spherical Symmetries in Euclidean Spaces PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Analysis of Spherical Symmetries in Euclidean Spaces PDF full book. Access full book title Analysis of Spherical Symmetries in Euclidean Spaces by Claus Müller. Download full books in PDF and EPUB format.
Author: Claus Müller
Publisher: Springer Science & Business Media
ISBN: 1461205816
Category : Mathematics
Languages : en
Pages : 227
Get Book
Book Description
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.
Author: Claus Müller
Publisher: Springer Science & Business Media
ISBN: 1461205816
Category : Mathematics
Languages : en
Pages : 227
Get Book
Book Description
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.
Author: Claus Muller
Publisher:
ISBN: 9781461205821
Category :
Languages : en
Pages : 240
Get Book
Book Description
Author: Audrey Terras
Publisher: Springer Science & Business Media
ISBN: 146147972X
Category : Mathematics
Languages : en
Pages : 430
Get Book
Book Description
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.
Author: Elias M. Stein
Publisher: Princeton University Press
ISBN: 9780691080789
Category : Mathematics
Languages : en
Pages : 318
Get Book
Book Description
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.
Author: Kendall Atkinson
Publisher: Springer Science & Business Media
ISBN: 3642259820
Category : Mathematics
Languages : en
Pages : 253
Get Book
Book Description
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.
Author: Gunter Ritter
Publisher: CRC Press
ISBN: 1439857970
Category : Computers
Languages : en
Pages : 389
Get Book
Book Description
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.
Author: Xue-Cheng Tai
Publisher: Springer Science & Business Media
ISBN: 3642022553
Category : Computers
Languages : en
Pages : 882
Get Book
Book Description
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.
Author: Takashi Washio
Publisher: Springer
ISBN: 364236778X
Category : Computers
Languages : en
Pages : 168
Get Book
Book Description
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.
Author: Gilles Aubert
Publisher: Springer Science & Business Media
ISBN: 0387445889
Category : Mathematics
Languages : en
Pages : 400
Get Book
Book Description
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.
Author: Brian Straughan
Publisher: Springer Science & Business Media
ISBN: 0387765433
Category : Technology & Engineering
Languages : en
Pages : 445
Get Book
Book Description
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.
