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arXiv · 2105.08641

Second-Order Differential Operators in the Limit Circle Case

Dmitri R. Yafaev
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Abstract

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 the theory of self-adjoint realizations of such operators by an analogy with the case of Jacobi operators. We introduce a new object, the quasiresolvent of the maximal operator, and use it to obtain a very explicit formula for the resolvents of all self-adjoint realizations. In particular, this yields a simple representation for the Cauchy-Stieltjes transforms of the spectral measures playing the role of the classical Nevanlinna formula in the theory of Jacobi operators.

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Dmitri R. Yafaev. 2021-05-18. Second-Order Differential Operators in the Limit Circle Case. https://doi.org/10.3842/sigma.2021.077

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