TY - JOUR

T1 - Dirac Operators with Exponentially Decaying Entropy

AU - Gubkin, P.

N1 - Export Date: 4 March 2024 Адрес для корреспонденции: Gubkin, P.; St. Petersburg State University, Universitetskaya Nab. 7-9, Russian Federation; эл. почта: gubkin.pv@yandex.ru Сведения о финансировании: Ministry of Education and Science of the Russian Federation, Minobrnauka, 075-15-2022-287 Текст о финансировании 1: The work is supported by Ministry of Science and Higher Education of the Russian Federation, agreement 075-15-2022-287 Пристатейные ссылки: Bessonov, R., Szegő condition and scattering for one-dimensional Dirac operators (2020) Constr. Approx, 51 (2), pp. 273-302. , 4076111; Bessonov, R., Denisov, S., De Branges canonical systems with finite logarithmic integral (2021) Anal. PDE, 14 (5), pp. 1509-1556. , 4307215; Bessonov, R., Denisov, S., Zero sets, entropy, and pointwise asymptotics of orthogonal polynomials (2021) J. Funct. Anal., 280 (12), p. 38. , 109002; Bessonov, R., Denisov, S., (2022) Sobolev Norms of L 2 -Solutions to NLS. Arxiv, 2211, p. 07051; Bessonov, R., Denisov, S., Szegő condition, scattering, and vibration of Krein strings (2023) Invent. Math, 234 (1), pp. 291-373. , 2023InMat.234.291B, 4635834; Damanik, D., Simon, B., Jost functions and Jost solutions for Jacobi matrices. II. Decay and analyticity (2006) Int. Math. Res. Not., Pages Art. ID, 19396, p. 32; Denisov, S., Continuous analogs of polynomials orthogonal on the unit circle and Kreĭn systems. IMRS (2006) Int. Math. Res. Surv., Pages Art. ID, 54517, p. 148; Dyatlov, S., Zworski, M., (2019) Mathematical Theory of Scattering Resonances. Graduate Studies in Mathematics, , Providence, RI, American Mathematical Society; Fried, H., (2002) Green’s Functions and Ordered Exponentials, , Cambridge, Cambridge University Press; Froese, R., Asymptotic distribution of resonances in one dimension (1997) J. Differ. Equ, 137 (2), pp. 251-272. , 1997JDE..137.251F, 1456597; Garnett, J., (1981) Bounded Analytic Functions. 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PY - 2024/2/21

Y1 - 2024/2/21

N2 - We prove that the Weyl function of the one-dimensional Dirac operator on the half-line R+ with exponentially decaying entropy extends meromorphically into the horizontal strip {0⩾Imz>-δ} for some δ>0 depending on the rate of decay. If the entropy decreases very rapidly then the corresponding Weyl function turns out to be meromorphic in the whole complex plane. In this situation we show that poles of the Weyl function (scattering resonances) uniquely determine the operator. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

AB - We prove that the Weyl function of the one-dimensional Dirac operator on the half-line R+ with exponentially decaying entropy extends meromorphically into the horizontal strip {0⩾Imz>-δ} for some δ>0 depending on the rate of decay. If the entropy decreases very rapidly then the corresponding Weyl function turns out to be meromorphic in the whole complex plane. In this situation we show that poles of the Weyl function (scattering resonances) uniquely determine the operator. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

KW - 34L40

KW - Dirac operator

KW - Entropy function

KW - Krein system

UR - https://www.mendeley.com/catalogue/3ad9a6fc-e275-3c7f-bab8-826845c93e67/

U2 - 10.1007/s00365-024-09678-0

DO - 10.1007/s00365-024-09678-0

M3 - статья

JO - Constructive Approximation

JF - Constructive Approximation

SN - 0176-4276

ER -