On the Wiener-Pitt phenomenon for algebra of Rajchman multipliers on Hardy space

2022/06/14 by Ohrysko, Przemysław, Wojciechowski, Michał, Zawalski, Bartłomiej
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2206.06958

Abstract

We show that any positive Rajchman measure of Minkowski dimension 0 has a non-natural spectrum as an element of the multiplier algebra of H¹₀(\T). The proof is based on the estimation of the norm of the convolution operator given by a singular measure on H₀¹(\T).

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