On unbounded commuting Jacobi operators and some related issues

Abstract

We consider the situations, when two unbounded operators generated by infinite Jacobi matrices, are self-adjoint and commute. It is found that if two Jacobi matrices formally commute, then two corresponding operators are either self-adjoint and commute, or admit a commuting self-adjoint extensions. In the latter case such extensions are explicitly described. Also, some necessary and sufficient conditions for self-adjointness of Jacobi operators are studied.

Keywords

• jacobi matrices
• self-adjoint extensions
• moment problem
• orthogonal polynomials
• 47b39
• 47a10
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