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Generalized Functions

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

Book Description
Integral Geometry and Representation Theory ...

Integral Geometry and Representation Theory

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.