Jensen measures and boundary values of plurisubharmonic functions
(2001) In Arkiv för Matematik 39(1). p.181-200- Abstract
- We study different classes of Jensen measures for plurisubharmonic functions, in particular the relation between Jensen measures for continuous functions and Jensen measures for upper bounded functions. We prove an approximation theorem for plurisubharmonic functions inB-regular domain. This theorem implies that the two classes of Jensen measures coincide inB-regular domains. Conversely we show that if Jensen measures for continuous functions are the same as Jensen measures for upper bounded functions and the domain is hyperconvex, the domain satisfies the same approximation theorem as above.
The paper also contains a characterisation in terms of Jensen measures of those continuous functions that are boundary values of a... (More) - We study different classes of Jensen measures for plurisubharmonic functions, in particular the relation between Jensen measures for continuous functions and Jensen measures for upper bounded functions. We prove an approximation theorem for plurisubharmonic functions inB-regular domain. This theorem implies that the two classes of Jensen measures coincide inB-regular domains. Conversely we show that if Jensen measures for continuous functions are the same as Jensen measures for upper bounded functions and the domain is hyperconvex, the domain satisfies the same approximation theorem as above.
The paper also contains a characterisation in terms of Jensen measures of those continuous functions that are boundary values of a continuous plurisubharmonic function. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1314618
- author
- Wikström, Frank LU
- publishing date
- 2001
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Arkiv för Matematik
- volume
- 39
- issue
- 1
- pages
- 181 - 200
- publisher
- Springer
- external identifiers
-
- scopus:0348168902
- ISSN
- 0004-2080
- DOI
- 10.1007/BF02388798
- language
- English
- LU publication?
- no
- id
- 61f38e3f-1a9b-46fa-9dcf-bde35b05a814 (old id 1314618)
- date added to LUP
- 2016-04-01 12:08:08
- date last changed
- 2022-01-26 23:19:36
@article{61f38e3f-1a9b-46fa-9dcf-bde35b05a814,
abstract = {{We study different classes of Jensen measures for plurisubharmonic functions, in particular the relation between Jensen measures for continuous functions and Jensen measures for upper bounded functions. We prove an approximation theorem for plurisubharmonic functions inB-regular domain. This theorem implies that the two classes of Jensen measures coincide inB-regular domains. Conversely we show that if Jensen measures for continuous functions are the same as Jensen measures for upper bounded functions and the domain is hyperconvex, the domain satisfies the same approximation theorem as above.<br/><br>
The paper also contains a characterisation in terms of Jensen measures of those continuous functions that are boundary values of a continuous plurisubharmonic function.}},
author = {{Wikström, Frank}},
issn = {{0004-2080}},
language = {{eng}},
number = {{1}},
pages = {{181--200}},
publisher = {{Springer}},
series = {{Arkiv för Matematik}},
title = {{Jensen measures and boundary values of plurisubharmonic functions}},
url = {{http://dx.doi.org/10.1007/BF02388798}},
doi = {{10.1007/BF02388798}},
volume = {{39}},
year = {{2001}},
}