6 citations · 18 across the 8 of their papers we have counts for
14 papers
Spectral transitions in some Rabi models
Grzegorz Świderski, Lech Zieliński
We consider the transition from discrete to continuous spectrum which occurs in some quantum Rabi models. We present recent developments of the subordinacy theory and their applica…
Sturm-Liouville operators with periodically modulated parameters. Part I: Regular case
Grzegorz Świderski, Bartosz Trojan
We introduce a new class of Sturm-Liouville operators with periodically modulated parameters. Their spectral properties depend on the monodromy matrix of the underlying periodic pr…
Asymptotic zeros' distribution of orthogonal polynomials with unbounded recurrence coefficients
Grzegorz Świderski, Bartosz Trojan
We study spectrum of finite truncations of unbounded Jacobi matrices with periodically modulated entries. In particular, we show that under some hypotheses a sequence of properly n…
Barrier nonsubordinacy and absolutely continuous spectrum of block Jacobi matrices
Marcin Moszyński, Grzegorz Świderski
We explore to what extent the relation between the absolute continuous spectrum and non-existence of subordinate generalized eigenvectors, known for scalar Jacobi operators, can be…
Christoffel functions for multiple orthogonal polynomials
Grzegorz Świderski, Walter Van Assche
We study weak asymptotic behaviour of the Christoffel--Darboux kernel on the main diagonal corresponding to multiple orthogonal polynomials. We show that under some hypotheses the…
Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case II
Grzegorz Świderski, Bartosz Trojan
We study Jacobi matrices with -periodically modulated recurrence coefficients when the sequence of -step transfer matrices is convergent to a non-trivial Jordan block. In par…