Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Generalized Functions, Volume 5 PDF full book. Access full book title Generalized Functions, Volume 5 by I. M. Gel′fand. Download full books in PDF and EPUB format.
Author: I. M. Gel′fand Publisher: American Mathematical Soc. ISBN: 1470426633 Category : Mathematics Languages : en Pages : 474
Book Description
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.
Author: I. M. Gel′fand Publisher: American Mathematical Soc. ISBN: 1470426633 Category : Mathematics Languages : en Pages : 474
Book Description
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.
Author: I. M. Gel'fand Publisher: Academic Press ISBN: 1483262251 Category : Mathematics Languages : en Pages : 468
Book Description
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.
Author: Peter Kuchment Publisher: American Mathematical Soc. ISBN: 1470437821 Category : Mathematics Languages : en Pages : 314
Book Description
This is the first of two volumes dedicated to the centennial of the distinguished mathematician Selim Grigorievich Krein. The companion volume is Contemporary Mathematics, Volume 734. Krein was a major contributor to functional analysis, operator theory, partial differential equations, fluid dynamics, and other areas, and the author of several influential monographs in these areas. He was a prolific teacher, graduating 83 Ph.D. students. Krein also created and ran, for many years, the annual Voronezh Winter Mathematical Schools, which significantly influenced mathematical life in the former Soviet Union. The articles contained in this volume are written by prominent mathematicians, former students and colleagues of Selim Krein, as well as lecturers and participants of Voronezh Winter Schools. They are devoted to a variety of contemporary problems in functional analysis, operator theory, several complex variables, topological dynamics, and algebraic, convex, and integral geometry.
Author: Moshe Carmeli Publisher: World Scientific ISBN: 1783261692 Category : Science Languages : en Pages : 411
Book Description
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.
Author: Gaik Ambartsoumian Publisher: World Scientific ISBN: 9811242453 Category : Mathematics Languages : en Pages : 248
Book Description
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.
Author: Eric Grinberg Publisher: American Mathematical Soc. ISBN: 0821811487 Category : Mathematics Languages : en Pages : 524
Book Description
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.
Author: Eduardo Bayro-Corrochano Publisher: Springer ISBN: 3319748300 Category : Technology & Engineering Languages : en Pages : 753
Book Description
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.
Author: I. M. Gel′fand
Author: I. M. Gel′fand
Author: I. M. Gel'fand
Author: I. M. Gel'fand
Author: Izrailʹ Moiseevich Gelʹfand
Author: Luis A. Santaló
Author: Peter Kuchment
Author: Moshe Carmeli
Author: Gaik Ambartsoumian
Author: Eric Grinberg
Author: Eduardo Bayro-Corrochano