Small Hankel operators on generalized Fock spaces

2017/12/14 by Carme Cascante, Joan Fàbrega, Cascante, Carme +5
Mathematics · #30H20 #47B10 #47B35 #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1712.05250

openalex publication_date 2017/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider Fock spaces F^p,ℓ_α of entire functions on \mathbb C associated to the weights e^-α|z|^2ℓ, where α>0 and ℓ is a positive integer. We compute explicitly the corresponding Bergman kernel associated to F^2,ℓ_α and, using an adequate factorization of this kernel, we characterize the boundedness and the compactness of the small Hankel operator \mathfrakh^ℓ_b,α on F^p,ℓ_α. Moreover, we also determine when \mathfrakh^ℓ_b,α is a Hilbert-Schmidt operator on F^2,ℓ_α.

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