Measures not charging semipolars and equations of Schrödinger type
Let \(X\) be a (Borel) right Markov process with distinguished excessive measure \(m\). The author establishes a bijection between a certain class of multiplicative functionals of \(X\) and the class of (equivalence classes of) measures on the state space of \(X\) charging no \(m\)-semipolar set. (Two such measures are equivalent provided they put the same mass on each finely open set.) The author then uses this bijection to study questions of existence and uniqueness for the Schrödinger-type equation \((q-L)u+ u\mu= f\), where \(q> 0\), \(L\) is the infinitesimal generator of \(X\), and \(f\) is a suitable function. This work generalizes an earlier study of \textit{J. Baxter}, \textit{G. Dal Maso} and \textit{U. Mosco} [Trans. Am. Math. Soc. 303, 1-38 (1987; Zbl 0627.60071)], and also extends work of \textit{K.-T. Sturm} [Forum Math. 4, No. 3, 257-297 (1992; Zbl 0745.60080)] and \textit{K. Kuwae} [ibid., to appear].
scientific article; zbMATH DE number 723922
scientific article