Smooth plurisubharmonic exhaustion functions on pseudo-convex domains in infinite dimensions
Complex Variables
2024-06-26 v2 Functional Analysis
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 method in infinite-dimensional complex analysis.
Keywords
Cite
@article{arxiv.2402.07077,
title = {Smooth plurisubharmonic exhaustion functions on pseudo-convex domains in infinite dimensions},
author = {Zhouzhe Wang and Xu Zhang},
journal= {arXiv preprint arXiv:2402.07077},
year = {2024}
}
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33 pages