Spectral asymptotics of periodic discrete Schrödinger operators, I

Article type: Research Article

Authors: van Mouche, P.

Affiliations: Landbouwuniversiteit Wageningen, Hollandseweg 1, Postbus 8130 , 6706 KN Wageningen, The Netherlands

Note: [] Correspondence to: P. van Mouche, Landbouwuniversiteit Wageningen, Hollandseweg 1, Postbus 8130, 6706 KN Wageningen, The Netherlands.

Abstract: Asymptotics, for coupling constant A tending to zero and to infinity, for the bands and gaps of the Schrödinger operator (HAg)(n)=g(n+1)+Abng(n)+g(n−1) on l2(Z) with periodic potential b are studied. In this context special attention is paid to ‘asymptotic spectral powers’. Three different perturbation techniques are used to obtain results. In this first paper the emphasis lies on results that can be obtained by a first-order degenerate or arbitrary-order non-degenerate Rayleigh–Schrödinger perturbation calculus.

DOI: 10.3233/ASY-1995-11303

Journal: Asymptotic Analysis, vol. 11, no. 3, pp. 263-287, 1995