C[superscript ∞] Scaling Asymptotics for the Spectral Projector of the Laplacian
This article concerns new off-diagonal estimates on the remainder and its derivatives in the pointwise Weyl law on a compact n-dimensional Riemannian manifold. As an application, we prove that near any non-self-focal point, the scaling limit of the spectral projector of the Laplacian onto frequency...
| Hoofdauteurs: | , |
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| Formaat: | Artikel |
| Taal: | English |
| Gepubliceerd in: |
Springer US
2018
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| Online toegang: | http://hdl.handle.net/1721.1/115816 https://orcid.org/0000-0001-5911-1432 |
| _version_ | 1826212790286680064 |
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| author | Canzani, Yaiza Hanin, Boris |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Canzani, Yaiza Hanin, Boris |
| author_sort | Canzani, Yaiza |
| collection | MIT |
| description | This article concerns new off-diagonal estimates on the remainder and its derivatives in the pointwise Weyl law on a compact n-dimensional Riemannian manifold. As an application, we prove that near any non-self-focal point, the scaling limit of the spectral projector of the Laplacian onto frequency windows of constant size is a normalized Bessel function depending only on n. Keywords: Spectral projector, Pointwise Weyl Law, Scaling limits, Laplace eigenfunctions, Non-self-focal points |
| first_indexed | 2024-09-23T15:37:57Z |
| format | Article |
| id | mit-1721.1/115816 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:37:57Z |
| publishDate | 2018 |
| publisher | Springer US |
| record_format | dspace |
| spelling | mit-1721.1/1158162022-09-29T15:10:23Z C[superscript ∞] Scaling Asymptotics for the Spectral Projector of the Laplacian Canzani, Yaiza Hanin, Boris Massachusetts Institute of Technology. Department of Mathematics Hanin, Boris This article concerns new off-diagonal estimates on the remainder and its derivatives in the pointwise Weyl law on a compact n-dimensional Riemannian manifold. As an application, we prove that near any non-self-focal point, the scaling limit of the spectral projector of the Laplacian onto frequency windows of constant size is a normalized Bessel function depending only on n. Keywords: Spectral projector, Pointwise Weyl Law, Scaling limits, Laplace eigenfunctions, Non-self-focal points 2018-05-23T16:45:21Z 2018-05-23T16:45:21Z 2017-05 2018-01-13T04:23:33Z Article http://purl.org/eprint/type/JournalArticle 1050-6926 1559-002X http://hdl.handle.net/1721.1/115816 Canzani, Yaiza, and Boris Hanin. “C[superscript ∞] Scaling Asymptotics for the Spectral Projector of the Laplacian.” The Journal of Geometric Analysis, vol. 28, no. 1, Jan. 2018, pp. 111–22. https://orcid.org/0000-0001-5911-1432 en http://dx.doi.org/10.1007/s12220-017-9812-5 The Journal of Geometric Analysis Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Mathematica Josephina, Inc. application/pdf Springer US Springer US |
| spellingShingle | Canzani, Yaiza Hanin, Boris C[superscript ∞] Scaling Asymptotics for the Spectral Projector of the Laplacian |
| title | C[superscript ∞] Scaling Asymptotics for the Spectral Projector of the Laplacian |
| title_full | C[superscript ∞] Scaling Asymptotics for the Spectral Projector of the Laplacian |
| title_fullStr | C[superscript ∞] Scaling Asymptotics for the Spectral Projector of the Laplacian |
| title_full_unstemmed | C[superscript ∞] Scaling Asymptotics for the Spectral Projector of the Laplacian |
| title_short | C[superscript ∞] Scaling Asymptotics for the Spectral Projector of the Laplacian |
| title_sort | c superscript ∞ scaling asymptotics for the spectral projector of the laplacian |
| url | http://hdl.handle.net/1721.1/115816 https://orcid.org/0000-0001-5911-1432 |
| work_keys_str_mv | AT canzaniyaiza csuperscriptscalingasymptoticsforthespectralprojectorofthelaplacian AT haninboris csuperscriptscalingasymptoticsforthespectralprojectorofthelaplacian |