TY - JOUR

T1 - On Rate of Convergence for Universality Limits

AU - Bessonov, R.

N1 - Export Date: 4 March 2024 Адрес для корреспонденции: Bessonov, R.; St. Petersburg State University, Universitetskaya Nab. 7-9, Russian Federation; эл. почта: bessonov@pdmi.ras.ru Сведения о финансировании: Russian Science Foundation, RSF, 19-71-30002 Текст о финансировании 1: The work is supported by grant RScF 19-71-30002 of the Russian Science Foundation. The author is a Young Russian Mathematics award winner and would like to thank its sponsors and jury. Пристатейные ссылки: Bessonov, R., Entropy function and orthogonal polynomials (2021) J. Approx. Theory, 272. , 4319329; Bessonov, R., Denisov, S., A spectral Szegő theorem on the real line (2020) Adv. Math, 359. , https://; 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). , 4234228; Bessonov, R., Denisov, S., Szegő condition, scattering, and vibration of Krein strings (2023) Invent. Math, 234 (1), pp. 291-373. , 2023InMat.234.291B, 4635834; Deift, P.A., (1999) Orthogonal polynomials and random matrices: A Riemann-Hilbert approach, , Volume 3 of Courant Lecture Notes in Mathematics. New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence; Eichinger, B., Lukic, M., Simanek, B., An Approach to Universality Using Weyl M -Functions; Findley, E., Universality for locally Szegő measures (2008) J. Approx. Theory, 155 (2), pp. 136-154. , 2477011; Kuijlaars, A.B.J., Vanlessen, M., Universality for eigenvalue correlations from the modified Jacobi unitary ensemble (2002) Int. Math. Res. Not, 30, pp. 575-1600. , 1912278; Lubinsky, D., A new approach to universality limits involving orthogonal polynomials (2009) Ann. Math. (2), 170 (2), pp. 915-939. , 2552113; Lubinsky, D.S., Universality limits in the bulk for arbitrary measures on compact sets (2008) J. Anal. Math, 106, pp. 373-394. , 2448991; Máté, A., Nevai, P., Totik, V., Szegő’s extremum problem on the unit circle (1991) Ann. Math. (2), 134 (2), pp. 433-453. , 1127481; Poltoratski, A., Pointwise convergence of the non-linear Fourier transform (2021) Preprint Arxiv; Simon, B., Orthogonal Polynomials on the Unit Circle (2004) Part 1: Classical Theory. Colloquium Publications, , American Mathematical Society; Simon, B., The Christoffel–Darboux kernel (2008) Perspectives in Partial Differential Equations, Harmonic Analysis and Applications, Volume 79 of Proc. Sympos. Pure Math., pp. 295-335. , American Mathematical Society, Providence; Totik, V., Universality under Szegő’s condition (2016) Can. Math. Bull, 59 (1), pp. 211-224

PY - 2024/2/21

Y1 - 2024/2/21

N2 - Given a probability measure μ on the unit circle T, consider the reproducing kernel kμ,n(z1,z2) in the space of polynomials of degree at most n-1 with the L2(μ)–inner product. Let u,v∈C. It is known that under mild assumptions on μ near ζ∈T, the ratio kμ,n(ζeu/n,ζev/n)/kμ,n(ζ,ζ) converges to a universal limit S(u, v) as n→∞. We give an estimate for the rate of this convergence for measures μ with finite logarithmic integral. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

AB - Given a probability measure μ on the unit circle T, consider the reproducing kernel kμ,n(z1,z2) in the space of polynomials of degree at most n-1 with the L2(μ)–inner product. Let u,v∈C. It is known that under mild assumptions on μ near ζ∈T, the ratio kμ,n(ζeu/n,ζev/n)/kμ,n(ζ,ζ) converges to a universal limit S(u, v) as n→∞. We give an estimate for the rate of this convergence for measures μ with finite logarithmic integral. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

KW - 42C05

KW - 46E22

KW - Entropy

KW - Reproducing kernels

KW - Szegő class

KW - Universality

UR - https://www.mendeley.com/catalogue/13eeef71-ba09-3f69-81fb-22452edc3f16/

U2 - 10.1007/s00020-024-02757-8

DO - 10.1007/s00020-024-02757-8

M3 - статья

VL - 96

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 1

ER -