Smooth plurisubharmonic exhaustion functions on pseudo-convex domains in infinite dimensions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914848477020160 |
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| author | Wang, Zhouzhe Zhang, Xu |
| author_facet | Wang, Zhouzhe Zhang, Xu |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_07077 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Smooth plurisubharmonic exhaustion functions on pseudo-convex domains in infinite dimensions Wang, Zhouzhe Zhang, Xu Complex Variables Functional Analysis 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. |
| title | Smooth plurisubharmonic exhaustion functions on pseudo-convex domains in infinite dimensions |
| topic | Complex Variables Functional Analysis |
| url | https://arxiv.org/abs/2402.07077 |