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A proof of Kahane's conjecture in the Wiener algebra
Przemysław Ohrysko
We prove Kahane's conjecture: if a continuous unimodular function on the circle satisfies as , , then $F(x)=e…
Norm-Controlled Inversion in Measure Algebras
Przemysław Ohrysko
We solve Nikolski's norm-controlled inversion problem for measure algebras of locally compact Abelian groups. For every there is a constant , independent of the gro…
Strongly small-2 sets that are not Riesz sets on compact abelian groups
Przemysław Ohrysko
We prove that every infinite compact abelian group admits a countably infinite proper set that is strongly small-2 but not Riesz. More precisely, …
Inversion problem in algebras of integrable functions with summable Fourier transforms
Przemysław Ohrysko
In this paper, we study the norm-controlled inversion problem in two classes of algebras of integrable functions. In contrast of the classical case of , we prove that thi…