Fourier multipliers for Levy-Khinchin-Scheinberg weights

Nikolai Nikolski
IMB, Université de Bordeaux 1

Date(s) : 10/02/2014   iCal
10 h 00 min - 11 h 00 min

In this talk, we present a class of weight functions w on the circle 𝕋, called Lévy–Khinchin–Schoenberg (LKS) weights, for which we are able to completely characterize (in terms of a capacitary inequality) all Fourier multipliers for the weighted space L2(𝕋,w). We show that the multiplier algebra is nontrivial if and only if 1/w ∈ L1(𝕋), and in this case multipliers satisfy the Spectral Localization Property (no “hidden spectrum”). On the other hand, the Muckenhoupt (A2) condition responsible for the basis property of exponentials (eikx) is more or less independent of the Spectral Localization Property and LKS requirements. Some more complicated compositions of LKS weights are considered as well.


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