Smooth plurisubharmonic exhaustion functions on pseudo-convex domains in infinite dimensions

2024/02/11 by Wang, Zhouzhe, Zhang, Xu
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2402.07077

Abstract

In this paper, by modifying significantly the Friedrichs-Gross mollifier technique and/or using the Lasry-Lions regularization technique together with some carefully chosen cut-off functions, for the first time we construct explicitly smooth exhaustion functions on any open subset and smooth plurisubharmonic exhaustion functions on any pseudo-convex domain in a typical Hilbert space, which enjoy delicate properties needed for the L² method in infinite-dimensional complex analysis.

Related

• Approximation and Bounded Plurisubharmonic Exhaustion Functions Beyond Lipschitz Domains
• Plurisubharmonic exhaustion functions and almost complex Stein structures
• Bounded Plurisubharmonic Exhaustion Functions for Lipschitz Pseudoconvex Domains in \mathbbCPⁿ
• On regularization of J-plurisubharmonic functions
• On plurisubharmonic defining functions for pseudoconvex domains in ℂ²