On the constant in a transference inequality for the vector-valued Fourier transform
Classical Analysis and ODEs
2016-04-07 v3 Functional Analysis
Abstract
The standard proof of the equivalence of Fourier type on R^d and on the torus T^d is usually stated in terms of an implicit constant, defined as the minimum of a sum of powers of sinc functions. In this note we compute this minimum explicitly.
Keywords
Cite
@article{arxiv.1512.03727,
title = {On the constant in a transference inequality for the vector-valued Fourier transform},
author = {Dion Gijswijt and Jan van Neerven},
journal= {arXiv preprint arXiv:1512.03727},
year = {2016}
}
Comments
An alternative proof of the main result for the special case that the parameter r is integral, due to Tom Koornwinder, has been included