Matches in SemOpenAlex for { <https://semopenalex.org/work/W4310648300> ?p ?o ?g. }
Showing items 1 to 73 of
73
with 100 items per page.
- W4310648300 abstract "Let $A$ be an elliptic pseudo-differential operator of order $m$ on a closed manifold $mathcal{X}$ of dimension $n>0$, formally positive self-adjoint with respect to some positive smooth density $dmu_mathcal{X}$. Then, the spectrum of $A$ is made up of a sequence of eigenvalues $(lambda_k)_{kgeq 1}$ whose corresponding eigenfunctions $(e_k)_{kgeq 1}$ are $C^infty$ smooth. Fix $sinmathbb{R}$ and define [ K_L^s(x,y)=sum_{0<lambda_kleq L}lambda_k^{-s} e_k(x)overline{e_k(y)}, .] We derive asymptotic formulae near the diagonal for the kernels $K_L^s(x,y)$ when $Lrightarrow +infty$ with fixed $s$. For $s=0$, $K^0_L$ is the kernel of the spectral projector studied by Hormander in cite{ho68}. In the present work we build on Hormander's result to study the kernels $K^s_L$. If $s<frac{n}{m}$, $K_L^s$ is of order $L^{-s+n/m}$ and near the diagonal, the rescaled leading term behaves like the Fourier transform of an explicit function of the symbol of $A$. If $s=frac{n}{m}$, under some explicit generic condition on the principal symbol of $A$, which holds if $A$ is a differential operator, the kernel has order $ln(L)$ and the leading term has a logarithmic divergence smoothed at scale $L^{-1/m}$. Our results also hold for elliptic differential Dirichlet eigenvalue problems." @default.
- W4310648300 created "2022-12-14" @default.
- W4310648300 creator A5049983992 @default.
- W4310648300 date "2018-01-22" @default.
- W4310648300 modified "2023-09-27" @default.
- W4310648300 title "Weighted local Weyl laws for elliptic operators" @default.
- W4310648300 doi "https://doi.org/10.48550/arxiv.1801.07598" @default.
- W4310648300 hasPublicationYear "2018" @default.
- W4310648300 type Work @default.
- W4310648300 citedByCount "0" @default.
- W4310648300 crossrefType "posted-content" @default.
- W4310648300 hasAuthorship W4310648300A5049983992 @default.
- W4310648300 hasBestOaLocation W43106483001 @default.
- W4310648300 hasConcept C10138342 @default.
- W4310648300 hasConcept C104317684 @default.
- W4310648300 hasConcept C114614502 @default.
- W4310648300 hasConcept C121332964 @default.
- W4310648300 hasConcept C128803854 @default.
- W4310648300 hasConcept C134306372 @default.
- W4310648300 hasConcept C158448853 @default.
- W4310648300 hasConcept C158693339 @default.
- W4310648300 hasConcept C162324750 @default.
- W4310648300 hasConcept C17020691 @default.
- W4310648300 hasConcept C182306322 @default.
- W4310648300 hasConcept C185592680 @default.
- W4310648300 hasConcept C2778113609 @default.
- W4310648300 hasConcept C33676613 @default.
- W4310648300 hasConcept C33923547 @default.
- W4310648300 hasConcept C55493867 @default.
- W4310648300 hasConcept C62520636 @default.
- W4310648300 hasConcept C70610323 @default.
- W4310648300 hasConcept C70915906 @default.
- W4310648300 hasConcept C86339819 @default.
- W4310648300 hasConceptScore W4310648300C10138342 @default.
- W4310648300 hasConceptScore W4310648300C104317684 @default.
- W4310648300 hasConceptScore W4310648300C114614502 @default.
- W4310648300 hasConceptScore W4310648300C121332964 @default.
- W4310648300 hasConceptScore W4310648300C128803854 @default.
- W4310648300 hasConceptScore W4310648300C134306372 @default.
- W4310648300 hasConceptScore W4310648300C158448853 @default.
- W4310648300 hasConceptScore W4310648300C158693339 @default.
- W4310648300 hasConceptScore W4310648300C162324750 @default.
- W4310648300 hasConceptScore W4310648300C17020691 @default.
- W4310648300 hasConceptScore W4310648300C182306322 @default.
- W4310648300 hasConceptScore W4310648300C185592680 @default.
- W4310648300 hasConceptScore W4310648300C2778113609 @default.
- W4310648300 hasConceptScore W4310648300C33676613 @default.
- W4310648300 hasConceptScore W4310648300C33923547 @default.
- W4310648300 hasConceptScore W4310648300C55493867 @default.
- W4310648300 hasConceptScore W4310648300C62520636 @default.
- W4310648300 hasConceptScore W4310648300C70610323 @default.
- W4310648300 hasConceptScore W4310648300C70915906 @default.
- W4310648300 hasConceptScore W4310648300C86339819 @default.
- W4310648300 hasLocation W43106483001 @default.
- W4310648300 hasLocation W43106483002 @default.
- W4310648300 hasLocation W43106483003 @default.
- W4310648300 hasLocation W43106483004 @default.
- W4310648300 hasLocation W43106483005 @default.
- W4310648300 hasOpenAccess W4310648300 @default.
- W4310648300 hasPrimaryLocation W43106483001 @default.
- W4310648300 hasRelatedWork W1575765233 @default.
- W4310648300 hasRelatedWork W1971238389 @default.
- W4310648300 hasRelatedWork W1977290209 @default.
- W4310648300 hasRelatedWork W1985407884 @default.
- W4310648300 hasRelatedWork W2037092406 @default.
- W4310648300 hasRelatedWork W2298926634 @default.
- W4310648300 hasRelatedWork W3093665591 @default.
- W4310648300 hasRelatedWork W3098898877 @default.
- W4310648300 hasRelatedWork W4287633820 @default.
- W4310648300 hasRelatedWork W4298858559 @default.
- W4310648300 isParatext "false" @default.
- W4310648300 isRetracted "false" @default.
- W4310648300 workType "article" @default.