The Young type theorem in weighted Fock spaces

Anton Baranov (1, 2) , Yurii Belov (3) , Alexander Borichev (4, 5)

1 Department of Mathematics and Mechanics
2 NRU HSE, faculty of mathematics
3 Chebyshev Laboratory
4 I2M - Institut de Mathématiques de Marseille
5 SPBU - Saint Petersburg State University

We prove that for every radial weighted Fock space, the system biorthogonal to a complete and minimal system of reproducing kernels is also complete under very mild regularity assumptions on the weight. This result generalizes a theorem by Young on reproducing kernels in the Paley-Wiener space and a recent result of Belov for the classical Bargmann-Segal-Fock space.

Mots clés: Fock spaces; Paley-Wiener space; Bargmann-Segal-Fock space; result of Belov

Domaines: Variables complexes [math.CV]; Analyse fonctionnelle [math.FA]

Anton Baranov, Yurii Belov, Alexander Borichev. The Young type theorem in weighted Fock spaces. Bulletin of the London Mathematical Society, 2018, 50 (2), pp.357-363. ⟨10.1112/blms.12144⟩. ⟨hal-02052047⟩