Riesz bases of reproducing kernels in Fock-type spaces

By A. Baranov, Y. Belov, A. Borichev. Journal of the Institute of Mathematics of Jussieu, 2009

48 citations recorded by the source corpus.

Abstract In a scale of Fock spaces $\mathcal{F}_\varphi$ with radial weights ϕ we study the existence of Riesz bases of (normalized) reproducing kernels. We prove that these spaces possess such bases if and only if ϕ(x) grows at most like (log x)2.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d5135d0e6aa4eb4dbe5ab72b2c24f896fb13648c

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In Applied Mathematics

1. Y. Belov
2. T. Mengestie
3. Kristian Seip
4. Chun-Kit Lai

In Mathematical Physics

1. Y. Belov
2. T. Mengestie
3. Kristian Seip

Citations in the corpus

• Discrete Hilbert transforms on sparse sequences (2009, background): “In view of the observations in the previous subsections, the results of Borichev and Lyubarskii clarify when a Fock-type space equals a de Branges space, that is, when the two spaces consist of the same entire functions and have equivalent norms.”