In a recent work of the author, a de Branges space was constructed, as well as an operator on it whose spectrum coincides with the set of nontrivial zeros of the Riemann zeta function after a rotation of the complex plane. Also the canonical system related to the de Branges space in question was constructed. In this paper, a natural factorization is exhibited for 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. Bibliography: 1 title.
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V. V. Kapustin, “The zero set of the Riemann zeta function as the point spectrum of an operator,” Algebra Analiz, 33, No. 4, 107–124 (2021); English. transl., St.Petersburg Math. J., 33, No. 4, 661–673 (2022).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 503, 2021, pp. 84–96.
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Kapustin, V.V. Five Hilbert Space Models Related to the Riemann Zeta Function. J Math Sci 268, 791–799 (2022). https://doi.org/10.1007/s10958-022-06219-7
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DOI: https://doi.org/10.1007/s10958-022-06219-7