Strong nonsubordinacy and absolutely continuous spectra for Sturm-Liouville equations

Clark, Steve; Hinton, Don

doi:10.57262/die/1370378430

Cited by 9 publications

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“…Consider two sequences a = (a n : n ∈ N 0 ) and b = (b n : n ∈ N 0 ) such that a n > 0 and b n ∈ R for all n ≥ 0. Let A be the closure in 2 on finitely supported sequences. The operator A is called Jacobi matrix and its Jacobi parameters are the sequences a and b.…”

Section: Introductionmentioning

confidence: 99%

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

Świderski

Trojan

2023

Constr Approx

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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.

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Section: Introductionmentioning

confidence: 99%

“…In view of [2] (see also [32] for a different proof in a more general setup) the condition (1.9) implies existence of positive constants c 1 , c 2 such that the density of μ, μ , satisfies…”

Section: Introductionmentioning

confidence: 99%

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

Świderski

Trojan

2023

Constr Approx

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Spectral theory—50 years of progress and a conclusion

Pearson

2001

Math Methods in App Sciences

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A Spectral Analysis for Self-Adjoint Operators Generated by a Class of Second Order Difference Equations

Clark

1996

Journal of Mathematical Analysis and Applications

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A qualitative spectral analysis for a class of second order difference equations is given. Central to the analysis of equations in this class is the observation that real-valued solutions exhibit a type of stable asymptotic behavior for certain real values of the spectral parameter. This asymptotic behavior leads to the characterization of the limit point and limit circle nature of these equations, and is used to show that a strong nonsubordinacy criterion is satisfied on subintervals of ‫ޒ‬ for equations of limit point type. These subintervals are part of the absolutely continuous spectrum of the self-adjoint realization of these equations. By other means, the nature of the discrete spectrum for these self-adjoint realizations is also discussed.

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Strong nonsubordinacy and absolutely continuous spectra for Sturm-Liouville equations

Cited by 9 publications

References 0 publications

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

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

Spectral theory—50 years of progress and a conclusion

A Spectral Analysis for Self-Adjoint Operators Generated by a Class of Second Order Difference Equations

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