The paper claims an infinite-dimensional de Branges space can be associated with a semi-infinite Jacobi matrix in the limit circle case, via the semi-infinite connecting operator.
Inverse of infinite hankel moment matricesSymmetry, Integrability and Geometry: Methods and Applications (SIGMA),14, 2018,
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Inverse problem for semi-infinite Jacobi matrices and associated Hilbert spaces of analytic functions
The paper claims an infinite-dimensional de Branges space can be associated with a semi-infinite Jacobi matrix in the limit circle case, via the semi-infinite connecting operator.