TY - JOUR

T1 - Chui’s conjecture in Bergman spaces

AU - Abakumov, Evgeny

AU - Borichev, Alexander

AU - Fedorovskiy, Konstantin

N1 - Abakumov, E., Borichev, A. & Fedorovskiy, K. Chui’s conjecture in Bergman spaces. Math. Ann. 379, 1507–1532 (2021). https://proxy.library.spbu.ru:2060/10.1007/s00208-020-02114-1

PY - 2021/4

Y1 - 2021/4

N2 - We solve an analog of Chui’s conjecture on the simplest fractions (i.e., sums of Cauchy kernels with unit coefficients) in weighted (Hilbert) Bergman spaces. Namely, for a wide class of weights, we prove that for every N, the simplest fractions with N poles on the unit circle have minimal norm if and only if the poles are equispaced on the circle. We find sharp asymptotics of these norms. Furthermore, we describe the closure of the simplest fractions in weighted Bergman spaces, using an L2 version of Thompson’s theorem on dominated approximation by simplest fractions.

AB - We solve an analog of Chui’s conjecture on the simplest fractions (i.e., sums of Cauchy kernels with unit coefficients) in weighted (Hilbert) Bergman spaces. Namely, for a wide class of weights, we prove that for every N, the simplest fractions with N poles on the unit circle have minimal norm if and only if the poles are equispaced on the circle. We find sharp asymptotics of these norms. Furthermore, we describe the closure of the simplest fractions in weighted Bergman spaces, using an L2 version of Thompson’s theorem on dominated approximation by simplest fractions.

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KW - POLYNOMIALS

KW - FIELDS

UR - http://www.scopus.com/inward/record.url?scp=85096331332&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/2dee0747-8598-3217-8586-bcd52878dfc2/

U2 - 10.1007/s00208-020-02114-1

DO - 10.1007/s00208-020-02114-1

M3 - Article

AN - SCOPUS:85096331332

VL - 379

SP - 1507

EP - 1532

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 3-4

ER -