Jensen measures in product harmonic spaces

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• 作者：Mohammad Alakhrass (1)
  
  1. Mathematics Department ; University of Sharjah ; Sharjah ; United Arab Emirates
  
• 关键词：Multiply superharmonic functions ; Jensen measures ; Extreme elements ; Balayaged measures ; Fine open set ; Primary 31B05 ; Secondary 31D05
• 刊名：Annali di Matematica Pura ed Applicata
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：194
• 期：2
• 页码：563-568
• 全文大小：122 KB
• 参考文献：1. Alakhrass, M (2012) Extension spaces for superharmonic functions and Jensen Measures. J. Math. Soc. Jpn. 64: pp. 263-272 CrossRef
  2. Brelot, M.: Lectures on Potential Theory, Tata Institute, No 19, Bombay 1960, re-issued (1967)
  3. Cole, BJ, Ransford, TJ (2001) Jensen measures and harmonic measures. J. Reine Angew. Math. 541: pp. 29-53
  4. Fuglede, B.: Finely Harmonic Functions, Lecture Notes in Math. 289. Springer, Berlin (1972)
  5. Gowrisankaran, KN (1966) Multiply harmonic functions. Nagoya Math. J. 28: pp. 27-48
  6. Hansen, W, Netuka, I (2012) Jensen measures in potential theory. Potential Anal. 37: pp. 79-90 CrossRef
  7. Roy, S (2008) Extreme Jensen measures. Ark. Mat. 46: pp. 153-182 CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1618-1891

文摘

Let \(\Omega _j \subset \mathbf {R}^{n_j}\,(j=1,2)\) be an open connected set; here if \(n_j=2\) , it is assumed that \(\Omega \) has a Green function. The concept of Jensen measure is extended to classes of multiply superharmonic functions on \(\Omega _1\times \Omega _2\) . It is proved that product of extreme Jensen measures on the component space is an extreme Jensen measure in the product space. The article is finished by raising a question that is left as an open problem for further investigation.