Abstract
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.
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Mocanu, G., Raşa, I. C 0-Semigroups Associated with Markov Operators. Mediterr. J. Math. 13, 353–363 (2016). https://doi.org/10.1007/s00009-014-0497-8
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DOI: https://doi.org/10.1007/s00009-014-0497-8