Spectral asymptotics of periodic elliptic operators
| dc.creator | Bratteli, Ola | |
| dc.creator | Jorgensen, Palle E. T. | |
| dc.creator | Robinson, Derek W. | |
| dc.date | 1997-07-11 | |
| dc.date.accessioned | 2026-07-07T09:13:49Z | |
| dc.date.available | 2026-07-07T09:13:49Z | |
| dc.description | We demonstrate that the structure of complex second-order strongly elliptic operators $H$ on ${\bf R}^d$ with coefficients invariant under translation by ${\bf Z}^d$ can be analyzed through decomposition in terms of versions $H_z$, $z\in{\bf T}^d$, of $H$ with $z$-periodic boundary conditions acting on $L_2({\bf I}^d)$ where ${\bf I}=[0,1>$. If the semigroup $S$ generated by $H$ has a Hölder continuous integral kernel satisfying Gaussian bounds then the semigroups $S^z$ generated by the $H_z$ have kernels with similar properties and $z\mapsto S^z$ extends to a function on ${\bf C}^d\setminus\{0\}$ which is analytic with respect to the trace norm. The sequence of semigroups $S^{(m),z}$ obtained by rescaling the coefficients of $H_z$ by $c(x)\to c(mx)$ converges in trace norm to the semigroup $\hat{S}^z$ generated by the homogenization $\hat{H}_z$ of $H_z$. These convergence properties allow asymptotic analysis of the spectrum of $H$. | |
| dc.description | 27 pages, LaTeX article style | |
| dc.identifier | https://arxiv.org/abs/funct-an/9707002 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9707002 | |
| dc.identifier | Math. Z. 232 (1999), 621--650 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152457 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 43A65, 22E45, 35H05, 22E25, 35B45, 42C05 | |
| dc.title | Spectral asymptotics of periodic elliptic operators | |
| dc.type | text |