Geometric conditions for multiple sampling and interpolation in the Fock space

Alexander Borichev (1) , Andreas Hartmann (2) , Karim Kellay (2) , Xavier Massaneda (3)

1 I2M - Institut de Mathématiques de Marseille
2 IMB - Institut de Mathématiques de Bordeaux
3 Departament de Matemàtica Aplicada i Anàlisi

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.

Mots clés: multiple interpolation; Fock space; multiple sampling; Riesz basis

Domaines: Variables complexes [math.CV]

Alexander Borichev, Andreas Hartmann, Karim Kellay, Xavier Massaneda. Geometric conditions for multiple sampling and interpolation in the Fock space. Advances in Mathematics, 2017, 304, pp.1262-1295. ⟨10.1016/j.aim.2016.09.019⟩. ⟨hal-01184573v2⟩