Singular equivariant asymptotics and Weyl’s law. On the distribution of eigenvalues of an invariant elliptic operator
We study the spectrum of an invariant, elliptic, classical pseudodifferential operator on a closed Riemannian manifold carrying an effective and isometric action of a compact, connected Lie group . Using resolution of singularities, we determine the asymptotic distribution of eigenvalues along the i...
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| Veröffentlicht in: | Journal für die reine und angewandte Mathematik 2016-07, Vol.2016 (716), p.29-101 |
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| container_issue | 716 |
| container_start_page | 29 |
| container_title | Journal für die reine und angewandte Mathematik |
| container_volume | 2016 |
| creator | Ramacher, Pablo |
| description | We study the spectrum of an invariant, elliptic, classical pseudodifferential operator on a closed Riemannian manifold
carrying an effective and isometric action of a compact, connected Lie group
. Using resolution of singularities, we determine the asymptotic distribution of eigenvalues along the isotypic components, and relate it to the reduction of the corresponding Hamiltonian flow, proving that the reduced spectral counting function satisfies Weyl’s law, together with an estimate for the remainder. |
| doi_str_mv | 10.1515/crelle-2014-0008 |
| format | Article |
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carrying an effective and isometric action of a compact, connected Lie group
. Using resolution of singularities, we determine the asymptotic distribution of eigenvalues along the isotypic components, and relate it to the reduction of the corresponding Hamiltonian flow, proving that the reduced spectral counting function satisfies Weyl’s law, together with an estimate for the remainder.</description><identifier>ISSN: 0075-4102</identifier><identifier>EISSN: 1435-5345</identifier><identifier>DOI: 10.1515/crelle-2014-0008</identifier><language>eng</language><publisher>De Gruyter</publisher><ispartof>Journal für die reine und angewandte Mathematik, 2016-07, Vol.2016 (716), p.29-101</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c367t-25771601b745f828f8a9171b0be8658b0dab90a5214964f247c7a0f4b0bcbc813</citedby><cites>FETCH-LOGICAL-c367t-25771601b745f828f8a9171b0be8658b0dab90a5214964f247c7a0f4b0bcbc813</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.degruyter.com/document/doi/10.1515/crelle-2014-0008/pdf$$EPDF$$P50$$Gwalterdegruyter$$H</linktopdf><linktohtml>$$Uhttps://www.degruyter.com/document/doi/10.1515/crelle-2014-0008/html$$EHTML$$P50$$Gwalterdegruyter$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,66754,68538</link.rule.ids></links><search><creatorcontrib>Ramacher, Pablo</creatorcontrib><title>Singular equivariant asymptotics and Weyl’s law. On the distribution of eigenvalues of an invariant elliptic operator</title><title>Journal für die reine und angewandte Mathematik</title><description>We study the spectrum of an invariant, elliptic, classical pseudodifferential operator on a closed Riemannian manifold
carrying an effective and isometric action of a compact, connected Lie group
. Using resolution of singularities, we determine the asymptotic distribution of eigenvalues along the isotypic components, and relate it to the reduction of the corresponding Hamiltonian flow, proving that the reduced spectral counting function satisfies Weyl’s law, together with an estimate for the remainder.</description><issn>0075-4102</issn><issn>1435-5345</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp1kE1OwzAUhC0EEqWwZ-kLpNiOHSfLquJPqtQFIJbRS-IUV64TbIcqO67B9TgJjgpLVm-eNDMafQhdU7Kggoqb2iljVMII5QkhJD9BM8pTkYiUi1M0I0SKhFPCztGF97voEFSyGTo8absdDDis3gf9AU6DDRj8uO9DF3TtMdgGv6rRfH9-eWzgsMAbi8Obwo32welqCLqzuGux0ltlP8AMyk8vWKztX2HcpvtYh7teOQidu0RnLRivrn7vHL3c3T6vHpL15v5xtVwndZrJkDAhJc0IrSQXbc7yNoeCSlqRSuWZyCvSQFUQEIzyIuMt47KWQFoeDXVV5zSdI3LsrV3nvVNt2Tu9BzeWlJQTuPIIrpzAlRO4GFkeIwcwQblGbd0wRlHuusHZOPbfaBRZnMuK9AfP9HsK</recordid><startdate>20160701</startdate><enddate>20160701</enddate><creator>Ramacher, Pablo</creator><general>De Gruyter</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20160701</creationdate><title>Singular equivariant asymptotics and Weyl’s law. On the distribution of eigenvalues of an invariant elliptic operator</title><author>Ramacher, Pablo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c367t-25771601b745f828f8a9171b0be8658b0dab90a5214964f247c7a0f4b0bcbc813</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ramacher, Pablo</creatorcontrib><collection>CrossRef</collection><jtitle>Journal für die reine und angewandte Mathematik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ramacher, Pablo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Singular equivariant asymptotics and Weyl’s law. On the distribution of eigenvalues of an invariant elliptic operator</atitle><jtitle>Journal für die reine und angewandte Mathematik</jtitle><date>2016-07-01</date><risdate>2016</risdate><volume>2016</volume><issue>716</issue><spage>29</spage><epage>101</epage><pages>29-101</pages><issn>0075-4102</issn><eissn>1435-5345</eissn><abstract>We study the spectrum of an invariant, elliptic, classical pseudodifferential operator on a closed Riemannian manifold
carrying an effective and isometric action of a compact, connected Lie group
. Using resolution of singularities, we determine the asymptotic distribution of eigenvalues along the isotypic components, and relate it to the reduction of the corresponding Hamiltonian flow, proving that the reduced spectral counting function satisfies Weyl’s law, together with an estimate for the remainder.</abstract><pub>De Gruyter</pub><doi>10.1515/crelle-2014-0008</doi><tpages>73</tpages></addata></record> |
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| ispartof | Journal für die reine und angewandte Mathematik, 2016-07, Vol.2016 (716), p.29-101 |
| issn | 0075-4102 1435-5345 |
| language | eng |
| recordid | cdi_crossref_primary_10_1515_crelle_2014_0008 |
| source | De Gruyter journals |
| title | Singular equivariant asymptotics and Weyl’s law. On the distribution of eigenvalues of an invariant elliptic operator |
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