TY  - JOUR
A1  - Baumgärtel, Hellmut
T1  - A Characteristic decay semigroup for the resonances of trace class perturbations with analyticity conditions of semibounded hamiltonians
JF  - International journal of theoretical physic
N2  - To asymptotic complete scattering systems {M(+) + V, M(+)} on H(+) := L(2)(R(+), K, d lambda), where M(+) is the multiplication operator on H(+) and V is a trace class operator with analyticity conditions, a decay semigroup is associated such that the spectrum of the generator of this semigroup coincides with the set of all resonances (poles of the analytic continuation of the scattering matrix into the lower half plane across the positive half line), i.e. the decay semigroup yields a "time-dependent" characterization of the resonances. As a counterpart a "spectral characterization" is mentioned which is due to the "eigenvalue-like" properties of resonances.
KW  - Resonances
KW  - Scattering theory
KW  - Lax-Phillips theory
KW  - Decay semigroups
Y1  - 2011
U6  - https://doi.org/10.1007/s10773-010-0533-9
SN  - 0020-7748
VL  - 50
IS  - 7
SP  - 2002
EP  - 2008
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Güneysu, Batu
A1  - Keller, Matthias
T1  - Scattering the Geometry of Weighted Graphs
JF  - Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics
N2  - Given two weighted graphs (X, b(k), m(k)), k = 1, 2 with b(1) similar to b(2) and m(1) similar to m(2), we prove a weighted L-1-criterion for the existence and completeness of the wave operators W-+/- (H-2, H-1, I-1,I-2), where H-k denotes the natural Laplacian in l(2)(X, m(k)) w.r.t. (X, b(k), m(k)) and I-1,I-2 the trivial identification of l(2)(X, m(1)) with l(2) (X, m(2)). In particular, this entails a general criterion for the absolutely continuous spectra of H-1 and H-2 to be equal.
KW  - Graphs
KW  - Laplacian
KW  - Scattering theory
Y1  - 2018
U6  - https://doi.org/10.1007/s11040-018-9285-1
SN  - 1385-0172
SN  - 1572-9656
VL  - 21
IS  - 3
PB  - Springer
CY  - Dordrecht
ER  -