TY  - JOUR
A1  - Klein, Markus
A1  - Leonard, Christian
A1  - Rosenberger, Elke
T1  - Agmon-type estimates for a class of jump processes
JF  - Mathematische Nachrichten
N2  - 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.
KW  - Decay of eigenfunctions
KW  - semiclassical Agmon estimate
KW  - Finsler distance
KW  - jump process
KW  - Dirichlet-form
Y1  - 2014
U6  - https://doi.org/10.1002/mana.201200324
SN  - 0025-584X
SN  - 1522-2616
VL  - 287
IS  - 17-18
SP  - 2021
EP  - 2039
PB  - Wiley-VCH
CY  - Weinheim
ER  - 
TY  - JOUR
A1  - Klein, Markus
A1  - Rama, Juliane
T1  - Time asymptotics of e(-ith(kappa)) for analytic matrices and analytic perturbation theory
JF  - Asymptotic analysis
N2  - 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.
KW  - resonances
KW  - exponential decay
KW  - long-time corrections
KW  - Fermi golden rule
KW  - analytic perturbation theory
Y1  - 2014
U6  - https://doi.org/10.3233/ASY-141226
SN  - 0921-7134
SN  - 1875-8576
VL  - 89
IS  - 3-4
SP  - 189
EP  - 233
PB  - IOS Press
CY  - Amsterdam
ER  -