Geometric conditions for multiple sampling and interpolation in the Fock space

TL;DR

This paper investigates the conditions under which sequences can be used for sampling and interpolation in Fock spaces with unbounded multiplicities, revealing that such sequences cannot be both sampling and interpolating as multiplicities grow infinitely.

Contribution

It establishes new geometric criteria for multiple sampling and interpolation in Fock spaces with unbounded multiplicities, and proves the non-existence of sequences that are both sampling and interpolating under these conditions.

Findings

No sequences are both sampling and interpolating when multiplicities tend to infinity.

Provides geometric conditions for multiple sampling and interpolation in Fock spaces.

Shows limitations of sequence properties in the context of unbounded multiplicities.

Abstract

We study multiple sampling, interpolation and uniqueness for the classical Fock spaces in the case of unbounded multiplicities. We show that there are no sequences which are simultaneously sampling and interpolating when the multiplicities tend to infinity.