Год выпуска: 2014 Автор: Susanna Dann Издательство: Scholars' Press Страниц: 100 ISBN: 9783639702767
Описание
One of the important questions related to any integral transform on a manifold M or on a homogeneous space G/K is the description of the image of a given space of functions. If M=G/K, where (G,K) is a Gelfand pair, then harmonic analysis on M is closely related to the representations of G and the direct integral decomposition of the space of square-integrable functions on M into irreducible representations of G. The n-dimensional Euclidean space can be realized as the quotient of the orientation preserving Euclidean motion group E(n) by the special orthogonal group SO(n). The pair (E(n), SO(n)) is a Gelfand pair. Hence this realization of the n-dimensional Euclidean space comes with its own natural Fourier transform derived from the representation theory of E(n). The representations of E(n) that are in the support of the Plancherel measure for the space of square-integrable functions on n-dimensional Euclidean space are parameterized by positive reals. We describe the image of smooth...
