Browsing by Subject "Banach algebra"

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Algebry funkcyjne i ich całkowe reprezentacje
(Data obrony: 2010-07-08) Ślęzak, Piotr
Wydział Matematyki Stosowanej
Access status: Open Access ,
Corona theorem for strictly pseudoconvex domains
(Wydawnictwa AGH, 2021) Gwizdek, Sebastian
Nearly 60 years have passed since Lennart Carleson gave his proof of Corona Theorem for unit disc in the complex plane. It was only recently that M. Kosiek and K. Rudol obtained the first positive result for Corona Theorem in multidimensional case. Using duality methods for uniform algebras the authors proved »abstract« Corona Theorem which allowed to solve Corona Problem for a wide class of regular domains. In this paper we expand Corona Theorem to strictly pseudoconvex domains with smooth boundaries.
Access status: Open Access ,
Description of the scattering data for Sturm-Liouville operators on the half-line
(Wydawnictwa AGH, 2019) Mikitûk, Âroslav Volodimirovič; Suŝik, Natalìâ Stepanìvna
We describe the set of the scattering data for self-adjoint Sturm-Liouville operators on the half-line with potentials belonging to $L_1(\mathbb{R}_+,\rho(x)\,\text{d} x)$, where $\rho:\mathbb{R}_+\to\mathbb{R}_+$ is a monotonically nondecreasing function from some family $\mathscr{R}$. In particular, R includes the functions $\rho(x)=(1+x)^{\alpha}$ with $\alpha \geq 1$.
Access status: Open Access ,
Inverse scattering problems for half-line Schrödinger operators and Banach algebras
(Wydawnictwa AGH, 2018) Mikitûk, Âroslav Volodimirovič; Suŝik, Natalìâ Stepanìvna
The inverse scattering problem for half-line Schrödinger operators with potentials from the Marchenko class is shown to be closely related to some Banach algebra of functions on the line. In particular, it is proved that the topological conditions in the Marchenko theorem can be replaced by the condition that the scattering function should belong to this Banach algebra.
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Postac funkcjonałów liniowo-multiplikatywnych w algebrze $L^{1}\mathbb{(R)}$
(Data obrony: 2011-07-06) Mateja, Arkadiusz
Wydział Matematyki Stosowanej
Access status: Restricted ,
Rachunek funkcyjny dla samosprzężonych operatorów ograniczonych
(Data obrony: 2017-07-12) Kaczmarczyk, Łukasz
Wydział Matematyki Stosowanej