Generalized Functions Volume 5 Integral Geometry And Representation Theory

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Generalized Functions, Volume 5

Author : I. M. Gel′fand
Publisher : American Mathematical Soc.
ISBN 13 : 1470426633
Total Pages : 474 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Generalized Functions, Volume 5 by : I. M. Gel′fand

Download or read book Generalized Functions, Volume 5 written by I. M. Gel′fand and published by American Mathematical Soc.. This book was released on 2016-04-19 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gel′fand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. The unifying idea of Volume 5 in the series is the application of the theory of generalized functions developed in earlier volumes to problems of integral geometry, to representations of Lie groups, specifically of the Lorentz group, and to harmonic analysis on corresponding homogeneous spaces. The book is written with great clarity and requires little in the way of special previous knowledge of either group representation theory or integral geometry; it is also independent of the earlier volumes in the series. The exposition starts with the definition, properties, and main results related to the classical Radon transform, passing to integral geometry in complex space, representations of the group of complex unimodular matrices of second order, and harmonic analysis on this group and on most important homogeneous spaces related to this group. The volume ends with the study of representations of the group of real unimodular matrices of order two.

Generalized Functions

Author : I. M. Gel'fand
Publisher :
ISBN 13 : 9781483229751
Total Pages : 449 pages
Book Rating : 4.2/5 (297 download)

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Book Synopsis Generalized Functions by : I. M. Gel'fand

Download or read book Generalized Functions written by I. M. Gel'fand and published by . This book was released on 1966 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral Geometry and Representation Theory ...

Integral Geometry and Representation Theory

Author : I. M. Gel'fand
Publisher : Academic Press
ISBN 13 : 1483262251
Total Pages : 468 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Integral Geometry and Representation Theory by : I. M. Gel'fand

Download or read book Integral Geometry and Representation Theory written by I. M. Gel'fand and published by Academic Press. This book was released on 2014-05-12 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Functions, Volume 5: Integral Geometry and Representation Theory is devoted to the theory of representations, focusing on the group of two-dimensional complex matrices of determinant one. This book emphasizes that the theory of representations is a good example of the use of algebraic and geometric methods in functional analysis, in which transformations are performed not on the points of a space, but on the functions defined on it. The topics discussed include Radon transform on a real affine space, integral transforms in the complex domain, and representations of the group of complex unimodular matrices in two dimensions. The properties of the Fourier transform on G, integral geometry in a space of constant curvature, harmonic analysis on spaces homogeneous with respect to the Lorentz Group, and invariance under translation and dilation are also described. This volume is suitable for mathematicians, specialists, and students learning integral geometry and representation theory.

Integral Geometry and Geometric Probability

Author : Luis A. Santaló
Publisher : Cambridge University Press
ISBN 13 : 0521523443
Total Pages : 426 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis Integral Geometry and Geometric Probability by : Luis A. Santaló

Download or read book Integral Geometry and Geometric Probability written by Luis A. Santaló and published by Cambridge University Press. This book was released on 2004-10-28 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic text on integral geometry now available in paperback in the Cambridge Mathematical Library.

Generalized Radon Transforms And Imaging By Scattered Particles: Broken Rays, Cones, And Stars In Tomography

Author : Gaik Ambartsoumian
Publisher : World Scientific
ISBN 13 : 9811242453
Total Pages : 248 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Generalized Radon Transforms And Imaging By Scattered Particles: Broken Rays, Cones, And Stars In Tomography by : Gaik Ambartsoumian

Download or read book Generalized Radon Transforms And Imaging By Scattered Particles: Broken Rays, Cones, And Stars In Tomography written by Gaik Ambartsoumian and published by World Scientific. This book was released on 2023-03-14 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: A generalized Radon transform (GRT) maps a function to its weighted integrals along a family of curves or surfaces. Such operators appear in mathematical models of various imaging modalities. The GRTs integrating along smooth curves and surfaces (lines, planes, circles, spheres, amongst others) have been studied at great lengths for decades, but relatively little attention has been paid to transforms integrating along non-smooth trajectories. Recently, an interesting new class of GRTs emerged at the forefront of research in integral geometry. The two common features of these transforms are the presence of a 'vertex' in their paths of integration (broken rays, cones, and stars) and their relation to imaging techniques based on physics of scattered particles (Compton camera imaging, single scattering tomography, etc).This book covers the relevant imaging modalities, their mathematical models, and the related GRTs. The discussion of the latter comprises a thorough exploration of their known mathematical properties, including injectivity, inversion, range description and microlocal analysis. The mathematical background required for reading most of the book is at the level of an advanced undergraduate student, which should make its content attractive for a large audience of specialists interested in imaging. Mathematicians may appreciate certain parts of the theory that are particularly elegant with connections to functional analysis, PDEs and algebraic geometry.

Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis

Author : Eric Grinberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821811487
Total Pages : 524 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis by : Eric Grinberg

Download or read book Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis written by Eric Grinberg and published by American Mathematical Soc.. This book was released on 2000 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings from the conference honoring the work of Leon Ehrenpreis. Professor Ehrenpreis worked in many different areas of mathematics and found connections among all of them. For example, one can find his analytic ideas in the context of number theory, geometric thinking within analysis, transcendental number theory applied to partial differential equations, and more. The conference brought together the communities of mathematicians working in the areas of interest to Professor Ehrenpreis and allowed them to share the research inspired by his work. The collection of articles here presents current research on PDEs, several complex variables, analytic number theory, integral geometry, and tomography. The work of Professor Ehrenpreis has contributed to basic definitions in these areas and has motivated a wealth of research results. This volume offers a survey of the fundamental principles that unified the conference and influenced the mathematics of Leon Ehrenpreis.

Geometric Algebra Applications Vol. I

Author : Eduardo Bayro-Corrochano
Publisher : Springer
ISBN 13 : 3319748300
Total Pages : 753 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Geometric Algebra Applications Vol. I by : Eduardo Bayro-Corrochano

Download or read book Geometric Algebra Applications Vol. I written by Eduardo Bayro-Corrochano and published by Springer. This book was released on 2018-06-20 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the Volume I Geometric Algebra for Computer Vision, Graphics and Neural Computing is to present a unified mathematical treatment of diverse problems in the general domain of artificial intelligence and associated fields using Clifford, or geometric, algebra. Geometric algebra provides a rich and general mathematical framework for Geometric Cybernetics in order to develop solutions, concepts and computer algorithms without losing geometric insight of the problem in question. Current mathematical subjects can be treated in an unified manner without abandoning the mathematical system of geometric algebra for instance: multilinear algebra, projective and affine geometry, calculus on manifolds, Riemann geometry, the representation of Lie algebras and Lie groups using bivector algebras and conformal geometry. By treating a wide spectrum of problems in a common language, this Volume I offers both new insights and new solutions that should be useful to scientists, and engineers working in different areas related with the development and building of intelligent machines. Each chapter is written in accessible terms accompanied by numerous examples, figures and a complementary appendix on Clifford algebras, all to clarify the theory and the crucial aspects of the application of geometric algebra to problems in graphics engineering, image processing, pattern recognition, computer vision, machine learning, neural computing and cognitive systems.

Theory and Applications of Differentiable Functions of Several Variables

Author :
Publisher : American Mathematical Soc.
ISBN 13 : 9780821831526
Total Pages : 276 pages
Book Rating : 4.8/5 (315 download)

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Book Synopsis Theory and Applications of Differentiable Functions of Several Variables by :

Download or read book Theory and Applications of Differentiable Functions of Several Variables written by and published by American Mathematical Soc.. This book was released on 1994 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection is the 14th in an ongoing series on differentiable functions of several variables, presenting recent contributions to a line of research begun by Sobolev in 1950. The papers study various spaces of differentiable functions of several real variables in Euclidean space, their imbeddings, equivalent normings, weighted estimates of derivatives, and traces on sets. Several questions of approximation in function spaces on the line, on a hyperboloid, and on Lobachevsky space are studied. Investigations of bilinear approximations are applied to estimates of the singular numbers of integral operators and widths. The authors also examine the asymptotics of the spectrum of elliptic systems, as well as the Dirichlet variational problem for a degenerate elliptic operator. Finally, a block method of solving Laplace's equation for nonanalytic boundary conditions is developed.

Tomography, Impedance Imaging, and Integral Geometry

Author : Eric Todd Quinto
Publisher : American Mathematical Soc.
ISBN 13 : 9780821896990
Total Pages : 300 pages
Book Rating : 4.8/5 (969 download)

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Book Synopsis Tomography, Impedance Imaging, and Integral Geometry by : Eric Todd Quinto

Download or read book Tomography, Impedance Imaging, and Integral Geometry written by Eric Todd Quinto and published by American Mathematical Soc.. This book was released on 1991 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most exciting features of tomography is the strong relationship between high-level pure mathematics (such as harmonic analysis, partial differential equations, microlocal analysis, and group theory) and applications to medical imaging, impedance imaging, radiotherapy, and industrial nondestructive evaluation. This book contains the refereed proceedings of the AMS-SIAM Summer Seminar on Tomography, Impedance Imaging, and Integral Geometry, held at Mount Holyoke College in June 1993. A number of common themes are found among the papers. Group theory is fundamental both to tomographic sampling theorems and to pure Radon transforms. Microlocal and Fourier analysis are important for research in all three fields. Differential equations and integral geometric techniques are useful in impedance imaging. In short, a common body of mathematics can be used to solve dramatically different problems in pure and applied mathematics. Radon transforms can be used to model impedance imaging problems. These proceedings include exciting results in all three fields represented at the conference.

The Gelfand Mathematical Seminars, 1990–1992

Author : L. Corwin
Publisher : Springer Science & Business Media
ISBN 13 : 1461203457
Total Pages : 239 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis The Gelfand Mathematical Seminars, 1990–1992 by : L. Corwin

Download or read book The Gelfand Mathematical Seminars, 1990–1992 written by L. Corwin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Seminar began in Moscow in November 1943 and has continued without interruption up to the present. We are happy that with this vol ume, Birkhiiuser has begun to publish papers of talks from the Seminar. It was, unfortunately, difficult to organize their publication before 1990. Since 1990, most of the talks have taken place at Rutgers University in New Brunswick, New Jersey. Parallel seminars were also held in Moscow, and during July, 1992, at IRES in Bures-sur-Yvette, France. Speakers were invited to submit papers in their own style, and to elaborate on what they discussed in the Seminar. We hope that readers will find the diversity of styles appealing, and recognize that to some extent this reflects the diversity of styles in a mathematical society. The principal aim was to have interesting talks, even if the topic was not especially popular at the time. The papers listed in the Table of Contents reflect some of the rich variety of ideas presented in the Seminar. Not all the speakers submit ted papers. Among the interesting talks that influenced the seminar in an important way, let us mention, for example, that of R. Langlands on per colation theory and those of J. Conway and J. McKay on sporadic groups. In addition, there were many extemporaneous talks as well as short discus sions.

Analysis of Divergence

Author : William Bray
Publisher : Springer Science & Business Media
ISBN 13 : 1461222362
Total Pages : 568 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Analysis of Divergence by : William Bray

Download or read book Analysis of Divergence written by William Bray and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 7th International Workshop in Analysis and its Applications (IWAA) was held at the University of Maine, June 1-6, 1997 and featured approxi mately 60 mathematicians. The principal theme of the workshop shares the title of this volume and the latter is a direct outgrowth of the workshop. IWAA was founded in 1984 by Professor Caslav V. Stanojevic. The first meeting was held in the resort complex Kupuri, Yugoslavia, June 1-10, 1986, with two pilot meetings preceding. The Organization Committee to gether with the Advisory Committee (R. P. Boas, R. R. Goldberg, J. P. Kahne) set forward the format and content of future meetings. A certain number of papers were presented that later appeared individually in such journals as the Proceedings of the AMS, Bulletin of the AMS, Mathematis chen Annalen, and the Journal of Mathematical Analysis and its Applica tions. The second meeting took place June 1-10, 1987, at the same location. At the plenary session of this meeting it was decided that future meetings should have a principal theme. The theme for the third meeting (June 1- 10, 1989, Kupuri) was Karamata's Regular Variation. The principal theme for the fourth meeting (June 1-10, 1990, Kupuri) was Inner Product and Convexity Structures in Analysis, Mathematical Physics, and Economics. The fifth meeting was to have had the theme, Analysis and Foundations, organized in cooperation with Professor A. Blass (June 1-10, 1991, Kupuri).

Integral Methods in Science and Engineering

Author : Barbara S Bertram
Publisher : CRC Press
ISBN 13 : 0429525109
Total Pages : 329 pages
Book Rating : 4.4/5 (295 download)

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Book Synopsis Integral Methods in Science and Engineering by : Barbara S Bertram

Download or read book Integral Methods in Science and Engineering written by Barbara S Bertram and published by CRC Press. This book was released on 2019-05-20 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on proceedings of the International Conference on Integral Methods in Science and Engineering, this collection of papers addresses the solution of mathematical problems by integral methods in conjunction with approximation schemes from various physical domains. Topics and applications include: wavelet expansions, reaction-diffusion systems, variational methods , fracture theory, boundary value problems at resonance, micromechanics, fluid mechanics, combustion problems, nonlinear problems, elasticity theory, and plates and shells.

Guide to Geometric Algebra in Practice

Author : Leo Dorst
Publisher : Springer Science & Business Media
ISBN 13 : 0857298119
Total Pages : 458 pages
Book Rating : 4.8/5 (572 download)

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Book Synopsis Guide to Geometric Algebra in Practice by : Leo Dorst

Download or read book Guide to Geometric Algebra in Practice written by Leo Dorst and published by Springer Science & Business Media. This book was released on 2011-08-28 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This highly practical Guide to Geometric Algebra in Practice reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. Topics and features: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the description of rigid body motion, interpolation and tracking, and image processing; reviews the employment of GA in theorem proving and combinatorics; discusses the geometric algebra of lines, lower-dimensional algebras, and other alternatives to 5-dimensional CGA; proposes applications of coordinate-free methods of GA for differential geometry.

Global Differential Geometry

Author : Alfred Gray
Publisher : American Mathematical Soc.
ISBN 13 : 0821827502
Total Pages : 490 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Global Differential Geometry by : Alfred Gray

Download or read book Global Differential Geometry written by Alfred Gray and published by American Mathematical Soc.. This book was released on 2001 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alfred Gray's work covered a great part of differential geometry. In September 2000, a remarkable International Congress on Differential Geometry was held in his memory in Bilbao, Spain. Mathematicians from all over the world, representing 24 countries, attended the event. This volume includes major contributions by well known mathematicians (T. Banchoff, S. Donaldson, H. Ferguson, M. Gromov, N. Hitchin, A. Huckleberry, O. Kowalski, V. Miquel, E. Musso, A. Ros, S. Salamon, L. Vanhecke, P. Wellin and J.A. Wolf), the interesting discussion from the round table moderated by J.-P. Bourguignon, and a carefully selected and refereed selection of the Short Communications presented at the Congress. This book represents the state of the art in modern differential geometry, with some general expositions of some of the more active areas: special Riemannian manifolds, Lie groups and homogeneous spaces, complex structures, symplectic manifolds, geometry of geodesic spheres and tubes and related problems, geometry of surfaces, and computer graphics in differential geometry.

Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications

Author : Alexey P Isaev
Publisher : World Scientific
ISBN 13 : 9811217424
Total Pages : 615 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications by : Alexey P Isaev

Download or read book Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications written by Alexey P Isaev and published by World Scientific. This book was released on 2020-07-16 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras.The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed.Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C[Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed.Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO↑(p, q) are studied. For this purpose, Clifford algebras in spaces Rp, q are introduced and representations of these algebras are discussed.

Theory of Differential Equations

Author : I. M. Gel'fand
Publisher : Academic Press
ISBN 13 : 1483262324
Total Pages : 233 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Theory of Differential Equations by : I. M. Gel'fand

Download or read book Theory of Differential Equations written by I. M. Gel'fand and published by Academic Press. This book was released on 2014-05-12 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Functions, Volume 3: Theory of Differential Equations focuses on the application of generalized functions to problems of the theory of partial differential equations. This book discusses the problems of determining uniqueness and correctness classes for solutions of the Cauchy problem for systems with constant coefficients and eigenfunction expansions for self-adjoint differential operators. The topics covered include the bounded operators in spaces of type W, Cauchy problem in a topological vector space, and theorem of the Phragmén-Lindelöf type. The correctness classes for the Cauchy problem, systems that are Petrovski?-correct, and generalized eigenfunctions of self-adjoint operators are also reviewed. This text likewise covers the differentiation of functionals of strongly and weakly bounded variation. This volume is beneficial to students and researchers interested in the theory of differential equations.

Group Theory & General Relativity

Author : Moshe Carmeli
Publisher : World Scientific
ISBN 13 : 1783261692
Total Pages : 411 pages
Book Rating : 4.7/5 (832 download)

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Book Synopsis Group Theory & General Relativity by : Moshe Carmeli

Download or read book Group Theory & General Relativity written by Moshe Carmeli and published by World Scientific. This book was released on 2000-11-15 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the only book on the subject of group theory and Einstein's theory of gravitation. It contains an extensive discussion on general relativity from the viewpoint of group theory and gauge fields. It also puts together in one volume many scattered, original works, on the use of group theory in general relativity theory.There are twelve chapters in the book. The first six are devoted to rotation and Lorentz groups, and their representations. They include the spinor representation as well as the infinite-dimensional representations. The other six chapters deal with the application of groups -particularly the Lorentz and the SL(2,C) groups — to the theory of general relativity. Each chapter is concluded with a set of problems.The topics covered range from the fundamentals of general relativity theory, its formulation as an SL(2,C) gauge theory, to exact solutions of the Einstein gravitational field equations. The important Bondi-Metzner-Sachs group, and its representations, conclude the book. The entire book is self-contained in both group theory and general relativity theory, and no prior knowledge of either is assumed.The subject of this book constitutes a relevant link between field theoreticians and general relativity theoreticians, who usually work rather independently of each other. The treatise is highly topical and of real interest to theoretical physicists, general relativists and applied mathematicians. It is invaluable to graduate students and research workers in quantum field theory, general relativity and elementary particle theory.