C 0-Semigroups Associated with Markov Operators

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• 作者：Gabriela Mocanu ; Ioan Raşa
• 关键词：Primary 47D06 ; Secondary 47D07 ; 47F05 ; 47B65 ; Markov operator ; second ; order elliptic differential operator ; Markov semigroup ; contraction semigroup
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：13
• 期：1
• 页码：353-363
• 全文大小：533 KB
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  9.Raşa I.: Positive operators, Feller semigroups and diffusion equations associated with Altomare projections. Conf. Sem. Mat. Univ. Bari 284, 26 (2002)
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• 作者单位：Gabriela Mocanu (1)
  Ioan Raşa (2)
  
  1. Astronomical Observatory Cluj-Napoca, Astronomical Institute of the Romanian Academy, Cireşilor Street 15, 400487, Cluj-Napoca, Romania
  2. Department of Mathematics, Technical University of Cluj-Napoca, Memorandumului Street 28, 400114, Cluj-Napoca, Romania
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454

文摘

We consider a Markov operator T on the space \({\fancyscript{C}(K,\mathbb{R})}\), where K is a compact convex subset of \({\mathbb{R}^d}\) . An elliptic second-order differential operator W is associated with T. As generator of a Markov semigroup \({(T(t))_{t\geq 0}}\) on \({\fancyscript{C}(K,\mathbb{R})}\), W was intensely investigated by Francesco Altomare and his school. In this paper we show that W generates also a semigroup \({(U(t))_{t\geq 0}}\) on \({L^2(K,\mathbb{C})}\) . The relationship between the two semigroups is studied. Mathematics Subject Classification Primary 47D06 Secondary 47D07 47F05 47B65