Scattering the Geometry of Weighted Graphs

  • Batu GüneysuEmail author
  • Matthias Keller


Given two weighted graphs (X, bk, mk), k = 1,2 with b1b2 and m1m2, we prove a weighted L1-criterion for the existence and completeness of the wave operators W±(H2, H1, I1,2), where Hk denotes the natural Laplacian in 2(X, mk) w.r.t. (X, bk, mk) and I1,2 the trivial identification of 2(X, m1) with 2(X, m2). In particular, this entails a general criterion for the absolutely continuous spectra of H1 and H2 to be equal.


Graphs Laplacian Scattering theory 

Mathematics Subject Classification (2010)

35P25 05C63 35P05 



The authors are grateful for various discussions and hints on the literature by Jonathan Breuer, Evgeny Korotyaev, Peter Stollmann and Francoise Truc. Furthermore, the second author acknowledges the support of this research by the DFG.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Institut für MathematikUniversität PotsdamPotsdamGermany

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