Abstract
We study the weighted Fock spaces in one and several complex variables. We evaluate the dimension of these spaces in terms of the weight function extending and completing earlier results by Rozenblum–Shirokov and Shigekawa.
Highlights
Let ψ be a plurisubharmonic function on Cn, n ≥ 1
The weighted Fock space Fψ2 is the space of entire functions f such that f
In this paper we study when the space Fψ2 is of finite dimension depending on the weight ψ
Summary
Let ψ be a plurisubharmonic function on Cn, n ≥ 1. In [8, Theorem 3.2], Rozenblum and Shirokov proposed a sufficient condition for the space Fψ2 to be of infinite dimension, when ψ is a subharmonic function. They claimed that if ψ is a finite subharmonic function on the complex plane such that the measure μ = ∆ψ is of infinite mass: (1.1) We improve Theorem A by presenting a weaker condition for the dimension of the Fock space Fψ2 to be infinite.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
