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Jensen measures and boundary values of plurisubharmonic functions

Wikström, Frank LU (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)
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author
publishing date
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
2009-05-19 12:38:24
date last changed
2018-06-10 03:46:49
@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},
  volume       = {39},
  year         = {2001},
}