Reduced Weyl asymptotics for pseudodifferential operators on bounded domains II. The compact group case
| dc.creator | Cassanas, Roch | |
| dc.creator | Ramacher, Pablo | |
| dc.date | 2007-10-01 | |
| dc.date.accessioned | 2026-07-07T08:33:10Z | |
| dc.date.available | 2026-07-07T08:33:10Z | |
| dc.description | Let $G\subset Ø(n)$ be a compact group of isometries acting on $n$-dimensional Euclidean space $\R^n$, and ${\bf{X}}$ a bounded domain in $\R^n$ which is transformed into itself under the action of $G$. Consider a symmetric, classical pseudodifferential operator $A_0$ in $Ł^2(\R^n)$ that commutes with the regular representation of $G$, and assume that it is elliptic on $\bf{X}$. We show that the spectrum of the Friedrichs extension $A$ of the operator $\mathrm{res} \circ A_0 \circ \mathrm{ext}: \CT({\bf{X}}) \to Ł^2({\bf{X}})$ is discrete, and using the method of the stationary phase, we derive asymptotics for the number $N_χ(λ)$ of eigenvalues of $A$ equal or less than $λ$ and with eigenfunctions in the $χ$-isotypic component of $Ł^2({\bf{X}})$ as $λ\to \infty$, giving also an estimate for the remainder term for singular group actions. Since the considered critical set is a singular variety, we recur to partial desingularization in order to apply the stationary phase theorem. | |
| dc.description | 30 pages. Part 2 of 2 | |
| dc.identifier | https://arxiv.org/abs/0710.0126 | |
| dc.identifier | http://arxiv.org/abs/0710.0126 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139033 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Spectral Theory | |
| dc.subject | 35P20; 47G30; 20C99 | |
| dc.title | Reduced Weyl asymptotics for pseudodifferential operators on bounded domains II. The compact group case | |
| dc.type | text |