# 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

- MathematicsSymmetry, 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

- MathematicsBulletin 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 → ∞.…

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