Geodesic
Five Hilbert space models related to the Riemann zeta function
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 49, Tome 503 (2021), pp. 84-96 
V. V. Kapustin. Five Hilbert space models related to the Riemann zeta function. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 49, Tome 503 (2021), pp. 84-96. http://geodesic.mathdoc.fr/item/ZNSL_2021_503_a4/
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     author = {V. V. Kapustin},
     title = {Five {Hilbert} space models related to the {Riemann} zeta function},
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     year = {2021},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_503_a4/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In a recent work of the author, a de Branges space was constructed, as well as an operator on it with spectrum, which coincides with the set of non-trivial zeros of the Riemann zeta function after a rotation of the complex plane. Also the canonical system corresponding to the de Branges space was constructed. In this paper we construct a natural factorization of the unitary operator that realizes the unitary correspondence between the Hilbert space of the canonical system and the de Branges space, as the superposition of four unitary operators.

[1] V. V. Kapustin, “Mnozhestvo nulei dzeta-funktsii Rimana kak tochechnyi spektr operatora”, Algebra i analiz, 33:4 (2021), 107–124 | MR