4 citations · 14 across the 14 of their papers we have counts for
18 papers
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…
Nevanlinna--Pick norms on scattered and Cantor spectra
Przemysław Ohrysko, Michał Wojciechowski
We introduce Nevanlinna--Pick norms associated with finite families of characters on a commutative semisimple Banach algebra and study the class of algebras for whi…
Wiener-Pitt sets for compact Abelian groups
Przemysław Ohrysko, Tom Sanders, Michał Wojciechowski
Suppose that is a compact Hausdorff Abelian group. We say is strongly continuous if for any and any that is closed and of infinite…
An invitation to cortex algebras and spectral permanence property
Przemysław Ohrysko
We initiate the study of cortex algebras (commutative Banach algebras with extendable multiplicative-linear functionals) and the spectral permanence property. In addition, we analy…
The $H^1(\T^d)$-multiplier norm of Rajchman measures, Zafran-type phenomena, and Walsh--Stieltjes series
Przemysław Ohrysko, Michał Wojciechowski, Bartłomiej Zawalski
We study convolution by complex Rajchman measures as Fourier multipliers on the mean-zero part of the classical isotropic Hardy space $H^1(\T^d)$. Our main technical result gives a…
Spectrally reasonable measures II
Przemysław Ohrysko, Michał Wojciechowski
A measure on a locally compact Abelian group is said to have a natural spectrum if its spectrum is equal to the closure of the range of the Fourier-Stieltjes transform. In this pap…
The spectral radius formula for Fourier-Stieltjes algebras
Przemysław Ohrysko, Maria Roginskaya
In this short note we first extend the validity of the spectral radius formula obtained in \cite{ag} to Fourier--Stieltjes algebras. The second part is devoted to showing that for…
Inversion problem in measure and Fourier-Stieltjes algebras
Przemysław Ohrysko, Mateusz Wasilewski
In this paper we study the inversion problem in measure and Fourier-Stieltjes algebras from qualitative and quantitative point of view extending the results obtained by N. Nikolski…
The uniform invariant approximation property for compact groups
Przemysław Ohrysko
In this short note we give a proof of the refined version of the uniform invariant approximation property for compact (non-commutative) groups following the Bourgain's approach.
Spectral theory of Fourier-Stieltjes algebras
Przemysław Ohrysko, Mateusz Wasilewski
In this paper we start studying spectral properties of the Fourier-Stieltjes algebras, largely following Zafran's work on the algebra of measures on a locally compact group. We sho…
Non-separability of the Gelfand space of measure algebras
P. Ohrysko, M. Wojciechowski, Colin C. Graham
We prove that there exists uncountably many pairwise disjoint open subsets of the Gelfand space of the measure algebra on any locally compact non-discrete abelian group which shows…
Spectrally reasonable measures
Przemysław Ohrysko, Michał Wojciechowski
In this paper we investigate the problems related to measures with a natural spectrum (equal to the closure of the set of the values of the Fourier-Stieltjes transform). Since it i…
An elementary proof of the decomposition of measures on the circle group
Przemysław Ohrysko
In this short note we give an elementary proof for the case of the circle group of the theorem of O. Hatori and E. Sato which states that every measure on the compact abelian group…
On the Gelfand space of the measure algebra on the circle group
Przemysław Ohrysko, Michał Wojciechowski
This paper is devoted to studying certain topological properties of the maximal ideal space of the measure algebra on the circle group. In particular, we focus on Cech cohomologies…
On the relationships between Fourier - Stieltjes coefficients and spectra of measures
Przemysław Ohrysko, Michał Wojciechowski
We construct examples of uncountable compact subsets of complex numbers with the property that any Borel measure on the circle group taking values of its Fourier coefficients from…