# Scattering the Geometry of Weighted Graphs

#### Autoren: Güneysu, Batu; Keller, Matthias (2018)

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.

Zeitschrift:
Math. Phys. Anal. Geom.
Seiten:
21-28
Band:
21

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