Browsing by Subject "operators"

Now showing 1 - 4 of 4

Access status: Restricted ,
Asymptotyczny rozkład wartości własnych dla pewnych macierzy typu Jacobiego
(Data obrony: 2014-07-10) Banach, Agnieszka
Wydział Matematyki Stosowanej
Access status: Open Access ,
Certain group dynamical systems induced by Hecke algebras
(2016) Cho, Ilwoo
In this paper, we study dynamical systems induced by a certain group $\mathfrak{T}_{N}^{K}$ embedded in the Hecke algebra $\mathcal{H}(G_{p})$ induced by the generalized linear group $G_{p} = GL_{2}(\mathbb{Q}_{p})$ over the p-adic number fields $\mathbb{Q}_{p}$ for a fixed prime $p$. We study fundamental properties of such dynamical systems and the corresponding crossed product algebras in terms of free probability on the Hecke algebra $\mathcal{H}(G_{p})$.
Access status: Open Access ,
Matrices defined by frames
(2009) Ambroziński, Zbigniew; Rudol, Krzysztof
Matrix representations of bounded Hilbert space operators are considered. The matrices in question are defined with respect to frames, rather than bases. The frames, a generalisation of bases, used extensively in applied harmonic analysis, are overcomplete sequences. We consider some properties related to tight frames, where, up to some multiplicative constant, a form of Parseval Identity takes place. We also describe parts of spectra of operators in terms of their matrices.
Access status: Open Access ,
Matrices related to some Fock space operators
(2011) Rudol, Krzysztof
Matrices of operators with respect to frames are sometimes more natural and easier to compute than the ones related to bases. The present work investigates such operators on the Segal-Bargmann space, known also as the Fock space. We consider in particular some properties of matrices related to Toeplitz and Hankel operators. The underlying frame is provided by normalised reproducing kernel functions at some lattice points.