I. M. Gel'fandM. I. GraevN. Ya. VilenkinMay 12, 2014

Academic PressGeneralized 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.

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.

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Publisher

Academic Press

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Published on

May 12, 2014

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Pages

468

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ISBN

9781483262253

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Language

English

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Genres

Mathematics / Calculus

Mathematics / Mathematical Analysis

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Content Protection

This content is DRM protected.

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Eligible for Family Library

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