Periodic perturbations of unbounded Jacobi matrices III: The soft edge regime

Świderski, Grzegorz

doi:10.1016/j.jat.2018.04.006

Cited by 12 publications

(3 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We should mention interesting recent works by G. Świderski [29,30,31,32] also devoted, in particular, to the study of the spectral density. However, these considerations did not include the Jordan box case.…”

Section: Introductionmentioning

confidence: 99%

Titchmarsh-Weyl formula for the spectral density of a class of Jacobi matrices in the critical case

Naboko¹,

Simonov²

2019

Preprint

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Titchmarsh-Weyl formula for the spectral density of a class of Jacobi matrices in the critical case

Naboko¹,

Simonov²

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…Therefore, by [24,Theorem D] and [24,Proposition 11], the measure μ is purely absolutely continuous on with positive continuous density proving the first assertion. Next, let us observe that, by (4.33),…”

Section: (433)mentioning

confidence: 68%

Asymptotic Behaviour of Christoffel–Darboux Kernel Via Three-Term Recurrence Relation I

Świderski

Trojan

2020

Constr Approx

Self Cite

View full text Add to dashboard Cite

For Jacobi parameters belonging to one of three classes: asymptotically periodic, periodically modulated, and the blend of these two, we study the asymptotic behavior of the Christoffel functions and the scaling limits of the Christoffel–Darboux kernel. We assume regularity of Jacobi parameters in terms of the Stolz class. We emphasize that the first class only gives rise to measures with compact supports.

show abstract

“…As it was shown in [40,Theorem 7.34] and [12,Theorem 6], if supp(μ) is compact, the asymptotic behavior of shifted Turán determinants is usually closely related to the density of μ, see [30,31] and the survey [41]. The extension of the above phenomena to measures with unbounded support has been accomplished in [54,55,57,61]. For these reasons the following theorem is an important result on its own.…”

Section: Introductionmentioning

confidence: 88%

Orthogonal Polynomials with Periodically Modulated Recurrence Coefficients in the Jordan Block Case II

Świderski

Trojan

2023

Constr Approx

Self Cite

View full text Add to dashboard Cite

We study Jacobi matrices with N-periodically modulated recurrence coefficients when the sequence of N-step transfer matrices is convergent to a non-trivial Jordan block. In particular, we describe asymptotic behavior of their generalized eigenvectors, we prove convergence of N-shifted Turán determinants as well as of the Christoffel–Darboux kernel on the diagonal. Finally, by means of subordinacy theory, we identify their absolutely continuous spectrum as well as their essential spectrum. By quantifying the speed of convergence of transfer matrices we were able to cover a large class of Jacobi matrices. In particular, those related to generators of birth–death processes.

show abstract

Periodic perturbations of unbounded Jacobi matrices III: The soft edge regime

Cited by 12 publications

References 23 publications

Titchmarsh-Weyl formula for the spectral density of a class of Jacobi matrices in the critical case

Titchmarsh-Weyl formula for the spectral density of a class of Jacobi matrices in the critical case

Asymptotic Behaviour of Christoffel–Darboux Kernel Via Three-Term Recurrence Relation I

Orthogonal Polynomials with Periodically Modulated Recurrence Coefficients in the Jordan Block Case II

Contact Info

Product

Resources

About