We establish a version of the Paaley-Wiener theorem of Fourier Analysis in the frame of Mellin transforms. We provide two different proofs, one involving complex analysis arguments, namely the Riemann surface of the logarithm and Cauchy theorems, and the other one employing a Bernstein inequality here derived for Mellin derivatives.
On the Paley-Wiener theorem in the Mellin transform setting
BARDARO, Carlo;MANTELLINI, Ilaria;
2016
Abstract
We establish a version of the Paaley-Wiener theorem of Fourier Analysis in the frame of Mellin transforms. We provide two different proofs, one involving complex analysis arguments, namely the Riemann surface of the logarithm and Cauchy theorems, and the other one employing a Bernstein inequality here derived for Mellin derivatives.File in questo prodotto:
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