English

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 L2L^{2} 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}
}

Comments

33 pages