On the differential and Volterra-type integral operators on Fock-type spaces

Authors

  • Tesfa Mengestie Mathematics Section, Western Norway University of Applied Sciences, Klingenbergvegen 8, N-5414 Stord, Norway

DOI:

https://doi.org/10.33044/revuma.2149

Abstract

The differential operator fails to admit some basic structures including continuity when it acts on the classical Fock spaces or weighted Fock spaces, where the weight functions grow faster than the classical Gaussian weight function. The same conclusion also holds in some weighted Fock spaces including the Fock-Sobolev spaces, where the weight functions grow more slowly than the Gaussian function. We consider modulating the classical weight function and identify Fock-type spaces where the operator admits the basic structures. We also describe some properties of Volterra-type integral operators on these spaces using the notions of order and type of entire functions. The modulation operation supplies richer structures for both the differential and integral operators in contrast to the classical setting.

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Published

2022-10-12