Geodesic
Inverse problem for semi-infinite Jacobi matrices and associated Hilbert spaces of analytic functions
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 51, Tome 536 (2024), pp. 156-177

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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. 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. 
@article{ZNSL_2024_536_a8,
     author = {A. Mikhailov and V. Mikhailov},
     title = {Inverse problem for semi-infinite {Jacobi} matrices and associated {Hilbert} spaces of analytic functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {156--177},
     publisher = {mathdoc},
     volume = {536},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_536_a8/}
}
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A. Mikhailov; V. Mikhailov. Inverse problem for semi-infinite Jacobi matrices and associated Hilbert spaces of analytic functions. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 51, Tome 536 (2024), pp. 156-177. http://geodesic.mathdoc.fr/item/ZNSL_2024_536_a8/