Fourier transform of function on locally compact Abelian groups taking value in Banach spaces

Details Fourier transform of function on locally compact Abelian groups taking value in Banach spaces Fourier transform of function on locally compact Abelian groups taking value in Banach spaces

2008-08-29

arxiv.org/abs/0808.4009v1

Mathematics

Functional Analysis

9 pages

Scientific paper

We consider Fourier transform of vector-valued functions on a locally compact group $G$, which take value in a Banach space $X$, and are square-integrable in Bochner sense. If $G$ is a finite group then Fourier transform is a bounded operator. If $G$ is an infinite group then Fourier transform $F: L_2(G,X)\to L_2(\widehat G,X)$ is a bounded operator if and only if Banach space $X$ is isomorphic to a Hilbert one.

Affiliated with

Also associated with

No associations

Rating

Fourier transform of function on locally compact Abelian groups taking value in Banach 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 Fourier transform of function on locally compact Abelian groups taking value in Banach spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fourier transform of function on locally compact Abelian groups taking value in Banach spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-542065