Generalized Functions PDF Download

Author: I. M. Gel'fand
Publisher:
ISBN: 9781483229751
Category : Theory of distributions (Functional analysis)
Languages : en
Pages : 449

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Integral Geometry and Representation Theory ...

Author: Izrail Moiseevich Gelfand
Publisher:
ISBN:
Category :
Languages : en
Pages : 18

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Author: I. M. Gel'fand
Publisher: Academic Press
ISBN: 1483262251
Category : Mathematics
Languages : en
Pages : 468

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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: I. M. Gel'fand
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author:
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ISBN:
Category :
Languages : en
Pages :

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Author: Izrailʹ M. Gelʹfand
Publisher:
ISBN:
Category :
Languages : en
Pages : 449

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Author: Izrail' M. Gel'fand
Publisher:
ISBN: 9780122794056
Category :
Languages : en
Pages : 0

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Author: Israe͏̈l Mojseevic Gel'fand
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author: I. M. Gel′fand
Publisher: American Mathematical Soc.
ISBN: 1470426633
Category : Mathematics
Languages : en
Pages : 474

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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: Izrailʹ Moiseevich Gelʹfand
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 480

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