Sampling in Spaces of Bandlimited Functions on Commutative Spaces

Details Sampling in Spaces of Bandlimited Functions on Commutative Spaces Sampling in Spaces of Bandlimited Functions on Commutative Spaces

2011-07-22

arxiv.org/abs/1107.4578v1

Mathematics

Functional Analysis

Scientific paper

A connected homogeneous space X=G/K is called commutative if G is a connected Lie group, $K$ is a compact subgroup and the B*-algebra L^1(X)^K of K-invariant integrable function on X is commutative. In this article we introduce the space L^2_A (X) of A-bandlimited function on X by using the spectral decomposition of L^2 (X). We show that those spaces are reproducing kernel Hilbert spaces and determine the reproducing kernel. We then prove sampling results for those spaces using the smoothness of the elements in L^2_A (X). At the end we discuss the example of R^d, the spheres S^d, compact symmetric spaces and the Heisenberg group realized as the commutative space U (n) x H_n/U (n).

Affiliated with

Also associated with

No associations

Rating

Sampling in Spaces of Bandlimited Functions on Commutative Spaces 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 Sampling in Spaces of Bandlimited Functions on Commutative Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sampling in Spaces of Bandlimited Functions on Commutative Spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-677163