Abstract
Let X={X t ,t≥0} be a symmetric Markov process in a state space E and D an open set of E. Let S(n)={S(n) t , t ≥ 0} be a subordinator with Laplace exponent ϕ n and S={S t ,t≥0} a subordinator with Laplace exponent ϕ. Suppose that X is independent of S and S(n). In this paper we consider the subordinate processes and and their subprocesses and Xϕ,D killed upon leaving D. Suppose that the spectra of the semigroups of and Xϕ,D are all discrete, with being the eigenvalues of the generator of and being the eigenvalues of the generator of Xϕ,D. We show that, if lim n →∞ϕ n (λ)=ϕ(λ) for every λ>0, then
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The research of this author is supported in part by NSF Grant DMS-0303310.
The research of this author is supported in part by a joint US-Croatia grant INT 0302167.
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Chen, ZQ., Song, R. Continuity of eigenvalues of subordinate processes in domains. Math. Z. 252, 71–89 (2006). https://doi.org/10.1007/s00209-005-0845-2
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DOI: https://doi.org/10.1007/s00209-005-0845-2