De Branges spaces and Fock spaces

Anton Baranov (1, 2) , Hélène Bommier-Hato (3, 4)

1 Department of Mathematics and Mechanics
2 National Research University Higher School of Economics [St. Petersburg]
3 I2M - Institut de Mathématiques de Marseille
4 University Vienna, Fac Math

Relations between two classes of Hilbert spaces of entire functions, de Branges spaces and Fock-type spaces with nonradial weights, are studied. It is shown that any de Branges space can be realized as a Fock-type space with equivalent area norm, and several constructions of a representing weight are suggested. For some special classes of weights (e.g. weights depending on the imaginary part only) the corresponding de Branges spaces are explicitly described.

Mots clés: Reproducing kernel Hilbert space; de Branges space; Hermite-Biehler class; Fock space; Hardy space; inner function; level set

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

Anton Baranov, Hélène Bommier-Hato. De Branges spaces and Fock spaces. Complex Variables and Elliptic Equations, 2018, 63 (7-8), pp.907-930. ⟨10.1080/17476933.2017.1409742⟩. ⟨hal-02015124⟩