scholarly journals Finite Sections of Random Jacobi Operators

2012 ◽  
Vol 50 (1) ◽  
pp. 287-306 ◽  
Author(s):  
Marko Lindner ◽  
Steffen Roch
Keyword(s):  
Jacobi Operators ◽  
Finite Sections

Finite sections: A functional analytic perspective on approximation methods

2018 ◽  
Vol 41 (3) ◽  
pp. e201800013 ◽  
Author(s):  
Marko Lindner ◽  
Christian Seifert
Keyword(s):  
Approximation Methods ◽  
Finite Sections

scholarly journals Second-Order Differential Operators in the Limit Circle Case

2021 ◽  
Author(s):  
Dmitri R. Yafaev ◽  
◽  
◽  
Keyword(s):  
Differential Equation ◽  
Differential Operators ◽  
Second Order ◽  
Spectral Measures ◽  
Limit Circle ◽  
Jacobi Operators ◽  
Limit Circle Case ◽  
Circle Case ◽  
Stieltjes Transforms

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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