Inverse problem for semi-infinite Jacobi matrices and associated Hilbert spaces of analytic functions

2025/05/13 by Mikhaylov, Alexander, Mikhaylov, Victor
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2505.08338

Abstract

We consider the dynamic problems for the discrete systems with discrete time associated with finite and semi-infinite Jacobi matrices. The result of the paper is a procedure of association of special Hilbert spaces of functions, namely de Branges space, playing an important role in the inverse spectral theory, with these systems. %Thus the procedure, offered by the authors in the %previous papers now is extended to the case of semi-infinite %Jacobi matrices. We point out the relationships with the classical moment problems theory and compare properties of classical Hankel matrices associated with moment problems with properties of matrices of connecting operators associated with dynamical systems.

Citations

• Closable Hankel operators and moment problems
• Inverse dynamic problems for canonical systems and de Branges spaces
• On a Hilbert space of entire functions
• Unbounded Hankel operators and moment problems
• Canonical systems and de Branges spaces
• Small eigenvalues of large Hankel matrices:The indeterminate case

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• On the complex moment problem as a dynamic inverse problem for a discrete system