Polynomials with exponents in compact convex sets and associated weighted extremal functions -- Approximations and regularity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908773624315904 |
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| author | Snorrason, Bergur |
| author_facet | Snorrason, Bergur |
| contents | We study various regularization operators on plurisubharmonic functions that preserve Lelong classes with growth given by certain compact convex sets. The purpose is to show that the weighted Siciak-Zakharyuta functions associated with these Lelong classes are lower semicontinuous. These operators are given by integral, infimal, and supremal convolutions. Continuity properties of the logarithmic supporting function are studied and a precise description is given of when it is uniformly continuous. This gives a contradiction to published results about the Hölder continuity of these Siciak-Zakharyuta functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20370 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polynomials with exponents in compact convex sets and associated weighted extremal functions -- Approximations and regularity Snorrason, Bergur Complex Variables 32U35 (Primary) 32U15 (Secondary) We study various regularization operators on plurisubharmonic functions that preserve Lelong classes with growth given by certain compact convex sets. The purpose is to show that the weighted Siciak-Zakharyuta functions associated with these Lelong classes are lower semicontinuous. These operators are given by integral, infimal, and supremal convolutions. Continuity properties of the logarithmic supporting function are studied and a precise description is given of when it is uniformly continuous. This gives a contradiction to published results about the Hölder continuity of these Siciak-Zakharyuta functions. |
| title | Polynomials with exponents in compact convex sets and associated weighted extremal functions -- Approximations and regularity |
| topic | Complex Variables 32U35 (Primary) 32U15 (Secondary) |
| url | https://arxiv.org/abs/2410.20370 |