Reduced Weyl asymptotics for pseudodifferential operators on bounded domains I. The finite group case
| dc.creator | Ramacher, Pablo | |
| dc.date | 2005-10-12 | |
| dc.date | 2007-07-21 | |
| dc.date.accessioned | 2026-07-07T08:19:31Z | |
| dc.date.available | 2026-07-07T08:19:31Z | |
| dc.description | Let $G\subset Ø(n)$ be a 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 $Ł^2(\R^n)$ with G-invariant Weyl symbol, and assume that it is semi-bounded from below. 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 derive asymptotics for the number $N_χ(λ)$ of eigenvalues of A less or equal $λ$ and with eigenfunctions in the $χ$-isotypic component of $Ł^2({\bf{X}})$, giving also an estimate for the remainder term in both cases where G is a finite, or, more generally, a compact group. In particular, we show that the multiplicity of each unitary irreducible representation in $Ł^2({\bf{X}})$ is asymptotically proportional to its dimension. | |
| dc.description | 32 pages, Part 1 of 2 | |
| dc.identifier | https://arxiv.org/abs/math/0510261 | |
| dc.identifier | http://arxiv.org/abs/math/0510261 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134785 | |
| 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 I. The finite group case | |
| dc.type | text |