Articles liés à Paley-Wiener theorems with respect to the spectral...

Paley-Wiener theorems with respect to the spectral parameter - Couverture souple

Dann, Susanna

 
9783639702767: Paley-Wiener theorems with respect to the spectral parameter
Couverture souple
ISBN 10 : 363970276X ISBN 13 : 9783639702767
Editeur : Scholars' Press, 2014

Synopsis

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 compactly supported functions under the Fourier transform with respect to the spectral parameter. Then we discuss an extension of our description to projective limits of corresponding function spaces.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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 compactly supported functions under the Fourier transform with respect to the spectral parameter. Then we discuss an extension of our description to projective limits of corresponding function spaces.

Biographie de l'auteur

Dr. Susanna Dann is a postdoctoral researcher at the University of Missouri, Columbia. Starting September 2014 she will be an assistant professor at the Technical University Vienna, Austria. She obtained her B.Sc. from the University of Applied Sciences Stuttgart, Germany in 2004 and her Ph.D. from LSU, Baton Rouge in 2011.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Scholars' Press
Date d'édition
2014
Langue
anglais
ISBN 10 
363970276X
ISBN 13 
9783639702767
Reliure
Broché
Nombre de pages
100
Coordonnées du fabricant
non disponible
Personne responsable
non disponible