Spectral asymptotics of periodic elliptic operators |
| |
Authors: | Ola Bratteli Palle E.T. Jørgensen Derek W. Robinson |
| |
Affiliation: | (1) Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra, ACT 0200, Australia (e-mail: Derek.Robinson@anu.edu.au), AU |
| |
Abstract: | We demonstrate that the structure of complex second-order strongly elliptic operators H on with coefficients invariant under translation by can be analyzed through decomposition in terms of versions , , of H with z-periodic boundary conditions acting on where . If the s emigroup S generated by H has a H?lder continuous integral kernel satisfying Gaussian bounds then the semigroups generated by the have kernels with similar properties and extends to a function on which is analytic with respect to the trace norm. The sequence of semigroups obtained by rescaling the coefficients of by converges in trace norm to the semigroup generated by the homogenization of . These convergence properties allow asymptotic analysis of the spectrum of H. Received September 1, 1998; in final form January 14, 1999 |
| |
Keywords: | Mathematics Subject Classification (1991):43A65 22E45 35H05 22E25 35B45 42C05 |
本文献已被 SpringerLink 等数据库收录! |
|