New York Journal of Mathematics
Volume 27 (2021), 1580-1596


Haodong Li and Mishko Mitkovski

Necessary density conditions for d-approximate interpolation sequences in the Bargmann-Fock space

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Published: November 29, 2021.
Keywords: Bargmann-Fock space, approximate interpolation set, reproducing kernel, concentration operator.
Subject: 30D15, 30E05, 46E22.

Inspired by Olevskii and Ulanovskii [12], we introduce the concept of d-approximate interpolation in weighted Bargmann-Fock spaces as a natural extension of the classical concept of interpolation. We then show that d-approximate interpolation sets satisfy a density condition, similar to the one that classical interpolation sets satisfy. More precisely, we show that the upper Beurling density of any $d$-approximate interpolation set must be bounded from above by 1/(1-d2).


Research of the second author was supported in part by National Science Foundation DMS grant number 1600874.

Author information

Haodong Li:
School of Computer Engineering and Data Science
Guangzhou City University of Technology
Office-314, B1-Hall
Guangzhou, Guangdong 510800, China


Mishko Mitkovski:
Department of Mathematical and Statistical Sciences
Clemson University
O-110 Martin Hall, Box 340975
Clemson, SC 29643, USA