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arXiv · 2402.07077

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

Zhouzhe Wang·Xu Zhang
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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 $L^{2}$ method in infinite-dimensional complex analysis.

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Zhouzhe Wang, Xu Zhang. 2024-02-11. Smooth plurisubharmonic exhaustion functions on pseudo-convex domains in infinite dimensions. https://arxiv.org/abs/2402.07077

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