Chui’s conjecture in Bergman spaces

Evgeny Abakumov, Alexander Borichev, Konstantin Fedorovskiy

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)1507-1532
JournalMathematische Annalen
Volume379
Issue number3-4
DOIs
StatePublished - Apr 2021

Scopus subject areas

  • Mathematics(all)

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