@article{GueneysuKeller2018,
  author    = {G{\"u}neysu, Batu and Keller, Matthias},
  title     = {Scattering the Geometry of Weighted Graphs},
  series = {Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics},
  volume    = {21},
  journal   = {Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics},
  number    = {3},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {1385-0172},
  doi       = {10.1007/s11040-018-9285-1},
  pages     = {15},
  year      = {2018},
  abstract  = {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.},
  language  = {en}
}
@article{Baumgaertel2011,
  author    = {Baumg{\"a}rtel, Hellmut},
  title     = {A Characteristic decay semigroup for the resonances of trace class perturbations with analyticity conditions of semibounded hamiltonians},
  series = {International journal of theoretical physic},
  volume    = {50},
  journal   = {International journal of theoretical physic},
  number    = {7},
  publisher = {Springer},
  address   = {New York},
  issn      = {0020-7748},
  doi       = {10.1007/s10773-010-0533-9},
  pages     = {2002 -- 2008},
  year      = {2011},
  abstract  = {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.},
  language  = {en}
}