22 citations · 133 across the 17 of their papers we have counts for
17 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…
Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case
Grzegorz Świderski, Bartosz Trojan
We study orthogonal polynomials with periodically modulated recurrence coefficients when lies on the hard edge of the spectrum of the corresponding periodic Jacobi matrix. In p…
About essential spectra of unbounded Jacobi matrices
Grzegorz Świderski, Bartosz Trojan
We study spectral properties of unbounded Jacobi matrices with periodically modulated or blended entries. Our approach is based on uniform asymptotic analysis of generalized eigenv…
Asymptotic behaviour of Christoffel-Darboux kernel via three-term recurrence relation II
Grzegorz Świderski, Bartosz Trojan
We study orthogonal polynomials with periodically modulated Jacobi parameters in the case when lies on the soft edge of the spectrum of the corresponding periodic Jacobi matrix…
Spectral properties of some complex Jacobi matrices
Grzegorz Świderski
We study spectral properties of bounded and unbounded complex Jacobi matrices. In particular, we formulate conditions assuring that the spectrum of the studied operators is continu…
Asymptotic behaviour of Christoffel-Darboux kernel via three-term recurrence relation I
Grzegorz Świderski, Bartosz Trojan
For Jacobi parameters belonging to one of the three classes: asymptotically periodic, periodically modulated and the blend of these two, we study the asymptotic behavior of the Chr…
Asymptotics of orthogonal polynomials with slowly oscillating recurrence coefficients
Grzegorz Świderski, Bartosz Trojan
We study solutions of three-term recurrence relations whose -step transfer matrices belong to the uniform Stolz class. In particular, we derive the first order of their uniform…
Periodic perturbations of unbounded Jacobi matrices III: The soft edge regime
Grzegorz Świderski
We present pretty detailed spectral analysis of Jacobi matrices with periodically modulated entries in the case when lies on the soft edge of the spectrum of the corresponding…
Spectral properties of block Jacobi matrices
Grzegorz Świderski
We study the spectral properties of bounded and unbounded Jacobi matrices whose entries are bounded operators on a complex Hilbert space. In particular, we formulate conditions ass…
Periodic perturbations of unbounded Jacobi matrices II: Formulas for density
Grzegorz Świderski
We give formulas for the density of the measure of orthogonality for orthonormal polynomials with unbounded recurrence coefficients. The formulas involve limits of appropriately sc…
Periodic perturbations of unbounded Jacobi matrices I: Asymptotics of generalized eigenvectors
Grzegorz Świderski, Bartosz Trojan
We study asymptotics of generalized eigenvectors associated with Jacobi matrices. Under weak conditions on the coefficients we identify when the matrices are self-adjoint and show…
Spectral properties of unbounded Jacobi matrices with almost monotonic weights
Grzegorz Świderski
We present an unified framework to identify spectra of Jacobi matrices. We give applications to long-standing conjecture of Chihara concerning one-quarter class of orthogonal polyn…