Open Access
Summer 2012 Dispersive estimates for matrix and scalar Schrödinger operators in dimension five
William R. Green
Illinois J. Math. 56(2): 307-341 (Summer 2012). DOI: 10.1215/ijm/1385129950

Abstract

We investigate the boundedness of the evolution operators eitH and eitH in the sense of L1L for both the scalar Schrödinger operator H=Δ+V and the non-selfadjoint matrix Schrödinger operator

H=[Δ+μV1V2V2Δμ+V1]

in dimension five. Here μ>0 and V1, V2 are real-valued decaying potentials. The matrix operator arises when linearizing about a standing wave in certain nonlinear partial differential equations. We apply some natural spectral assumptions on H, including regularity of the edges of the spectrum ±μ.

Citation

Download Citation

William R. Green. "Dispersive estimates for matrix and scalar Schrödinger operators in dimension five." Illinois J. Math. 56 (2) 307 - 341, Summer 2012. https://doi.org/10.1215/ijm/1385129950

Information

Published: Summer 2012
First available in Project Euclid: 22 November 2013

zbMATH: 1373.35266
MathSciNet: MR3161326
Digital Object Identifier: 10.1215/ijm/1385129950

Subjects:
Primary: 35Q41 , 42B20

Rights: Copyright © 2012 University of Illinois at Urbana-Champaign

Vol.56 • No. 2 • Summer 2012
Back to Top