• Corpus ID: 233423319

Self-adjoint Jacobi operators in the limit circle case

@inproceedings{DRYafaev2021SelfadjointJO,
  title={Self-adjoint Jacobi operators in the limit circle case},
  author={D.R.Yafaev},
  year={2021}
}
We consider symmetric Jacobi operators with recurrence coefficients such that the corresponding difference equation is in the limit circle case. Equivalently, this means that the associated moment problem is indeterminate. Our main goal is to find a representation for the resolvents of self-adjoint realizations J of such Jacobi operators. This representation implies the classical Nevanlinna formula for the Cauchy-Stieltjes transforms of the spectral measures of the operators J . We also… 
2 Citations

Second-Order Differential Operators in the Limit Circle Case

  • D. Yafaev
  • Mathematics
    Symmetry, Integrability and Geometry: Methods and Applications
  • 2021
We consider symmetric second-order differential operators with real coefficients such that the corresponding differential equation is in the limit circle case at infinity. Our goal is to construct

Spectral analysis of Jacobi operators and asymptotic behavior of orthogonal polynomials

  • D. Yafaev
  • Mathematics
    Bulletin of Mathematical Sciences
  • 2022
We find and discuss asymptotic formulas for orthonormal polynomials Pn(z) with recurrence coefficients an, bn. Our main goal is to consider the case where off-diagonal elements an → ∞ as n → ∞.

References

SHOWING 1-10 OF 14 REFERENCES

The Classical Moment Problem as a Self-Adjoint Finite Difference Operator

Abstract This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna

Semiclassical asymptotic behavior of orthogonal polynomials

  • D. Yafaev
  • Mathematics
    Letters in Mathematical Physics
  • 2020
Our goal is to find asymptotic formulas for orthonormal polynomials $$P_{n}(z)$$ P n ( z ) with the recurrence coefficients slowly stabilizing as $$n\rightarrow \infty $$ n → ∞ . To that end, we

On the moment problem

The purpose of this paper is to provide some additional insight into the moment problem by connecting a condition by Lin, Bondesson's class of hyperbolically completely monotone densities, and the

Asymptotic behavior of orthogonal polynomials without the Carleman condition

  • D. Yafaev
  • Mathematics
    Journal of Functional Analysis
  • 2020

The Classical Moment Problem and Some Related Questions in Analysis

Setting here u = v, we see that |s + (v)| = |s − (v)|. There exists a vector v 0 ∈ D(J) such that s − (v 0 ) = 0 because J = clos J min . Let us set ω = s + (v 0 )/s − (v 0 )

    The moment problem, Graduate Texts in Mathematics, Springer, 2017

    • 2017

    Generalized Jacobi matrices and deficiency indices of differential operators with polynomial coefficients

    • Funct. Anal. Appl. 33, No
    • 1999