A duality theorem for certain fock spaces

TL;DR

This paper characterizes the dual spaces of certain weighted entire functions in complex analysis, focusing on functions with specific integrability and growth conditions related to subharmonic weights and Laplacian regularization.

Contribution

It provides a duality theorem for a class of Fock spaces involving subharmonic weights and regularized Laplacian, extending previous characterizations.

Findings

Explicit dual space descriptions for these Fock spaces.

Conditions under which the duality holds for 0<p≤1.

Connections between subharmonic weights and Laplacian regularization.

Abstract

We characterise functions for the dual spaces of entire functions f such that fe^{-\phi}\in L^p(\C^n,\rho^{-2}dA), 0<p\leq 1, where \phi is a subharmonic weight and \rho^{-2} is a positive function called under certain conditions regularised version of Laplacian \Delta\phi, as described in \cite{C}.