On the Constant in a Transference Inequality for the Vector-valued Fourier Transform

Gijswijt, DC; van Neerven, J.M.A.M.

On the Constant in a Transference Inequality for the Vector-valued Fourier Transform

Journal article (2016)

Authors

DC Gijswijt Discrete Mathematics and Optimization -

J.M.A.M. van Neerven Analysis -

Research Group

Discrete Mathematics and Optimization () (TU Delft)

Hausdorff-Young inequality 42B10 (46B20, 46E40)

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Published Date

2016

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Discrete Mathematics and Optimization

Abstract

The standard proof of the equivalence of Fourier type on Rd and on the torus Td 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.