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- W2952575203 abstract "Let $(X_t)_{tge 0}$ be a symmetric strong Markov process generated by non-local regular Dirichlet form $(D,D(D))$ as follows begin{equation*} begin{split} & D(f,g)=int_{R^d}int_{R^d}big(f(x)-f(y)big)big(g(x)-g(y)big) J(x,y),dx,dy, quad f,gin D(D) end{split} end{equation*} where $J(x,y)$ is a strictly positive and symmetric measurable function on $R^dtimes R^d$. We study the intrinsic hypercontractivity, intrinsic supercontractivity and intrinsic ultracontractivity for the Feynman-Kac semigroup $$ T^V_t(f)(x)=Ee^xleft(expBig(-int_0^tV(X_s),dsBig)f(X_t)right),,, xinR^d, fin L^2(R^d;dx).$$ In particular, we prove that for $$J(x,y)asymp|x-y|^{-d-alpha}I_{{|x-y|le 1}}+e^{-|x-y|}I_{{|x-y|> 1}}$$ with $alpha in (0,2)$ and $V(x)=|x|^lambda$ with $lambda>0$, $(T_t^V)_{tge 0}$ is intrinsically ultracontractive if and only if $lambda>1$; and that for symmetric $alpha$-stable process $(X_t)_{tge0}$ with $alpha in (0,2)$ and $V(x)=log^lambda(1+|x|)$ with some $lambda>0$, $(T_t^V)_{tge 0}$ is intrinsically ultracontractive (or intrinsically supercontractive) if and only if $lambda>1$, and $(T_t^V)_{tge 0}$ is intrinsically hypercontractive if and only if $lambdage1$. Besides, we also investigate intrinsic contractivity properties of $(T_t^V)_{t ge 0}$ for the case that $liminf_{|x| to infty}V(x)<infty$." @default.
- W2952575203 created "2019-06-27" @default.
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- W2952575203 date "2015-01-25" @default.
- W2952575203 modified "2023-09-23" @default.
- W2952575203 title "Intrinsic Contractivity of Feynman-Kac Semigroups for Symmetric Jump Processes with Infinite Range Jumps" @default.
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