@article{KleinLeonardRosenberger2014,
  author    = {Klein, Markus and Leonard, Christian and Rosenberger, Elke},
  title     = {Agmon-type estimates for a class of jump processes},
  series = {Mathematische Nachrichten},
  volume    = {287},
  journal   = {Mathematische Nachrichten},
  number    = {17-18},
  publisher = {Wiley-VCH},
  address   = {Weinheim},
  issn      = {0025-584X},
  doi       = {10.1002/mana.201200324},
  pages     = {2021 -- 2039},
  year      = {2014},
  abstract  = {In the limit 0 we analyse the generators H of families of reversible jump processes in Rd associated with a class of symmetric non-local Dirichlet-forms and show exponential decay of the eigenfunctions. The exponential rate function is a Finsler distance, given as solution of a certain eikonal equation. Fine results are sensitive to the rate function being C2 or just Lipschitz. Our estimates are analogous to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice Zd. Although our final interest is in the (sub)stochastic jump process, technically this is a pure analysis paper, inspired by PDE techniques.},
  language  = {en}
}
@article{KleinRama2014,
  author    = {Klein, Markus and Rama, Juliane},
  title     = {Time asymptotics of e(-ith(kappa)) for analytic matrices and analytic perturbation theory},
  series = {Asymptotic analysis},
  volume    = {89},
  journal   = {Asymptotic analysis},
  number    = {3-4},
  publisher = {IOS Press},
  address   = {Amsterdam},
  issn      = {0921-7134},
  doi       = {10.3233/ASY-141226},
  pages     = {189 -- 233},
  year      = {2014},
  abstract  = {In quantum mechanics the temporal decay of certain resonance states is associated with an effective time evolution e(-ith(kappa)), where h(.) is an analytic family of non-self-adjoint matrices. In general the corresponding resonance states do not decay exponentially in time. Using analytic perturbation theory, we derive asymptotic expansions for e(-ith(kappa)), simultaneously in the limits kappa -> 0 and t -> infinity, where the corrections with respect to pure exponential decay have uniform bounds in one complex variable kappa(2)t. In the Appendix we briefly review analytic perturbation theory, replacing the classical reference to the 1920 book of Knopp [Funktionentheorie II, Anwendungen und Weiterfuhrung der allgemeinen Theorie, Sammlung Goschen, Vereinigung wissenschaftlicher Verleger Walter de Gruyter, 1920] and its terminology by standard modern references. This might be of independent interest.},
  language  = {en}
}