Paley-Wiener Theorems with respect to the spectral parameter

Details Paley-Wiener Theorems with respect to the spectral parameter Paley-Wiener Theorems with respect to the spectral parameter

2010-12-08

arxiv.org/abs/1012.1801v1

Mathematics

Representation Theory

35 pages

Scientific paper

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 the harmonic analysis is closely related to the representations of G and the direct integral decomposition of L^2(M) into irreducible representations. We give a short overview of the Fourier transform on such spaces and then ask if one can describe the image of the space of smooth compactly supported functions in terms of the spectral parameter, i.e., the parameterization of the set of irreducible representations in the support of the Plancherel measure for L^2(M). We then discuss the Euclidean motion group, semisimple symmetric spaces, and some limits of those spaces.

Affiliated with

Also associated with

No associations

Rating

Paley-Wiener Theorems with respect to the spectral parameter does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Paley-Wiener Theorems with respect to the spectral parameter, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Paley-Wiener Theorems with respect to the spectral parameter will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-558817