Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

A simple method of calculating eigenvalues and resonances in domains with infinite regular ends

Michael Levitina1 and Marco Marlettaa2

a1 School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, UK (levitin@cardiff.ac.uk)

a2 School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, UK (marlettam@cardiff.ac.uk)

A new approach is presented for the solution of spectral problems on infinite domains with regular ends, which avoids the need to solve boundary-value problems for many trial values of the spectral parameter. We present numerical results both for eigenvalues and for resonances, comparing with results reported by Aslanyan, Parnovski and Vassiliev.

(Received November 20 2006)

(Accepted August 17 2007)