Two new Weyl-type bounds for the Dirichlet Laplacian
Trans. Amer. Math. Soc. 360 (2008), 1539-1558 In this paper, we prove two new Weyl-type upper estimates for the eigenvalues of the Dirichlet Laplacian. As a consequence, we obtain the following {\em lower} bounds for its counting function. For $\la\ge \la_1$, one has N(\la) > \dfrac{2}{n+2} \dfra...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | |
| container_volume | |
| creator | Hermi, Lotfi |
| description | Trans. Amer. Math. Soc. 360 (2008), 1539-1558 In this paper, we prove two new Weyl-type upper estimates for the eigenvalues
of the Dirichlet Laplacian. As a consequence, we obtain the following {\em
lower} bounds for its counting function. For $\la\ge \la_1$, one has
N(\la) > \dfrac{2}{n+2} \dfrac{1}{H_n} (\la-\la_1)^{n/2} \la_1^{-n/2},
and
N(\la) > (\dfrac{n+2}{n+4})^{n/2} \dfrac{1}{H_n} (\la-(1+4/n) \la_1)^{n/2}
\la_1^{-n/2},
where
H_n=\dfrac{2 n}{j_{n/2-1,1}^2 J_{n/2}^2(j_{n/2-1,1})}
is a constant which depends on $n$, the dimension of the underlying space,
and Bessel functions and their zeros. |
| doi_str_mv | 10.48550/arxiv.0711.4067 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_0711_4067</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>0711_4067</sourcerecordid><originalsourceid>FETCH-LOGICAL-a657-b996389132729505c8b2043f6ca9967490c38084f45cc10e023522c4ae291c23</originalsourceid><addsrcrecordid>eNotzjtrwzAUhmEtHULaPVPRH7B7dLOkMaSXBAwZGuhojk9lInBso7hN_e-b2_QNL3w8jC0E5NoZAy-Y_uJvDlaIXENhZ0zvTj3vwol_hanNxmkIvO5_uu8jb_rEx33grzFF2rdh5CUOLVLE7pE9NNgew9N95-zz_W23Wmfl9mOzWpYZFsZmtfeFcl4oaaU3YMjVErRqCsJzsdoDKQdON9oQCQgglZGSNAbpBUk1Z8-31yu6GlI8YJqqC7664NU_9MI8kg</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Two new Weyl-type bounds for the Dirichlet Laplacian</title><source>arXiv.org</source><creator>Hermi, Lotfi</creator><creatorcontrib>Hermi, Lotfi</creatorcontrib><description>Trans. Amer. Math. Soc. 360 (2008), 1539-1558 In this paper, we prove two new Weyl-type upper estimates for the eigenvalues
of the Dirichlet Laplacian. As a consequence, we obtain the following {\em
lower} bounds for its counting function. For $\la\ge \la_1$, one has
N(\la) > \dfrac{2}{n+2} \dfrac{1}{H_n} (\la-\la_1)^{n/2} \la_1^{-n/2},
and
N(\la) > (\dfrac{n+2}{n+4})^{n/2} \dfrac{1}{H_n} (\la-(1+4/n) \la_1)^{n/2}
\la_1^{-n/2},
where
H_n=\dfrac{2 n}{j_{n/2-1,1}^2 J_{n/2}^2(j_{n/2-1,1})}
is a constant which depends on $n$, the dimension of the underlying space,
and Bessel functions and their zeros.</description><identifier>DOI: 10.48550/arxiv.0711.4067</identifier><language>eng</language><subject>Mathematics - Mathematical Physics ; Mathematics - Spectral Theory ; Physics - Mathematical Physics</subject><creationdate>2007-11</creationdate><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,777,882</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/0711.4067$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.0711.4067$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Hermi, Lotfi</creatorcontrib><title>Two new Weyl-type bounds for the Dirichlet Laplacian</title><description>Trans. Amer. Math. Soc. 360 (2008), 1539-1558 In this paper, we prove two new Weyl-type upper estimates for the eigenvalues
of the Dirichlet Laplacian. As a consequence, we obtain the following {\em
lower} bounds for its counting function. For $\la\ge \la_1$, one has
N(\la) > \dfrac{2}{n+2} \dfrac{1}{H_n} (\la-\la_1)^{n/2} \la_1^{-n/2},
and
N(\la) > (\dfrac{n+2}{n+4})^{n/2} \dfrac{1}{H_n} (\la-(1+4/n) \la_1)^{n/2}
\la_1^{-n/2},
where
H_n=\dfrac{2 n}{j_{n/2-1,1}^2 J_{n/2}^2(j_{n/2-1,1})}
is a constant which depends on $n$, the dimension of the underlying space,
and Bessel functions and their zeros.</description><subject>Mathematics - Mathematical Physics</subject><subject>Mathematics - Spectral Theory</subject><subject>Physics - Mathematical Physics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzjtrwzAUhmEtHULaPVPRH7B7dLOkMaSXBAwZGuhojk9lInBso7hN_e-b2_QNL3w8jC0E5NoZAy-Y_uJvDlaIXENhZ0zvTj3vwol_hanNxmkIvO5_uu8jb_rEx33grzFF2rdh5CUOLVLE7pE9NNgew9N95-zz_W23Wmfl9mOzWpYZFsZmtfeFcl4oaaU3YMjVErRqCsJzsdoDKQdON9oQCQgglZGSNAbpBUk1Z8-31yu6GlI8YJqqC7664NU_9MI8kg</recordid><startdate>20071126</startdate><enddate>20071126</enddate><creator>Hermi, Lotfi</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20071126</creationdate><title>Two new Weyl-type bounds for the Dirichlet Laplacian</title><author>Hermi, Lotfi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a657-b996389132729505c8b2043f6ca9967490c38084f45cc10e023522c4ae291c23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Mathematics - Mathematical Physics</topic><topic>Mathematics - Spectral Theory</topic><topic>Physics - Mathematical Physics</topic><toplevel>online_resources</toplevel><creatorcontrib>Hermi, Lotfi</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Hermi, Lotfi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Two new Weyl-type bounds for the Dirichlet Laplacian</atitle><date>2007-11-26</date><risdate>2007</risdate><abstract>Trans. Amer. Math. Soc. 360 (2008), 1539-1558 In this paper, we prove two new Weyl-type upper estimates for the eigenvalues
of the Dirichlet Laplacian. As a consequence, we obtain the following {\em
lower} bounds for its counting function. For $\la\ge \la_1$, one has
N(\la) > \dfrac{2}{n+2} \dfrac{1}{H_n} (\la-\la_1)^{n/2} \la_1^{-n/2},
and
N(\la) > (\dfrac{n+2}{n+4})^{n/2} \dfrac{1}{H_n} (\la-(1+4/n) \la_1)^{n/2}
\la_1^{-n/2},
where
H_n=\dfrac{2 n}{j_{n/2-1,1}^2 J_{n/2}^2(j_{n/2-1,1})}
is a constant which depends on $n$, the dimension of the underlying space,
and Bessel functions and their zeros.</abstract><doi>10.48550/arxiv.0711.4067</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | DOI: 10.48550/arxiv.0711.4067 |
| ispartof | |
| issn | |
| language | eng |
| recordid | cdi_arxiv_primary_0711_4067 |
| source | arXiv.org |
| subjects | Mathematics - Mathematical Physics Mathematics - Spectral Theory Physics - Mathematical Physics |
| title | Two new Weyl-type bounds for the Dirichlet Laplacian |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-20T20%3A54%3A30IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Two%20new%20Weyl-type%20bounds%20for%20the%20Dirichlet%20Laplacian&rft.au=Hermi,%20Lotfi&rft.date=2007-11-26&rft_id=info:doi/10.48550/arxiv.0711.4067&rft_dat=%3Carxiv_GOX%3E0711_4067%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |