Jensen measures and boundary values of plurisubharmonic functions
(2001) In Arkiv för matematik 39(1). p.181200 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 inBregular domain. This theorem implies that the two classes of Jensen measures coincide inBregular 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 inBregular domain. This theorem implies that the two classes of Jensen measures coincide inBregular 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:
http://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
 00042080
 DOI
 10.1007/BF02388798
 language
 English
 LU publication?
 no
 id
 61f38e3f1a9b46fa9dcfbde35b05a814 (old id 1314618)
 date added to LUP
 20090519 12:38:24
 date last changed
 20180114 03:29:35
@article{61f38e3f1a9b46fa9dcfbde35b05a814, 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 inBregular domain. This theorem implies that the two classes of Jensen measures coincide inBregular 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 = {00042080}, language = {eng}, number = {1}, pages = {181200}, 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}, }