De Branges spaces and Fock spaces

2018/01/04 by Baranov, Anton, Bommier-Hato, Hélène
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1801.01345

Abstract

Relations between two classes of Hilbert spaces of entire functions, de Branges spaces and Fock-type spaces with non-radial 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.

Related

• On the dimension of the Fock type spaces
• Riesz bases of reproducing kernels in Fock type spaces and de Branges spaces
• The Fock space as a de Branges-Rovnyak space
• Some aspects of vector valued de Branges spaces of entire functions
• A de Branges-Beurling theorem for the full Fock space