Compactness of symmetric Markov semigroups and boundedness of eigenfunctions
Masayoshi Takeda · Transactions of the American Mathematical Society · 2018
Let X X be an irreducible m m -symmetric Markov process on E E with strong Feller property. In addition, suppose X X has a tightness property. We then show that the semigroup of X X is a compact operator on L 2 ( E ; m ) L^2(E;m) and every eigenfunction has a bounded continuous version.