On the Spectral Asymptotics of Operators on Manifolds with Ends
We deal with the asymptotic behaviour, for λ→+∞, of the counting function NP(λ) of certain positive self-adjoint operators P with double order (m,μ), m,μ > 0, m≠μ , defined on a manifold with ends M. The structure of this class of noncompact manifolds allows to make use of calculi of pseudodiffe...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/909782 |
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| author | Sandro Coriasco Lidia Maniccia |
| author_facet | Sandro Coriasco Lidia Maniccia |
| author_sort | Sandro Coriasco |
| collection | DOAJ |
| description | We deal with the asymptotic behaviour, for λ→+∞, of the counting
function NP(λ) of certain positive self-adjoint operators P with double order (m,μ), m,μ > 0, m≠μ
, defined on a manifold with ends M. The structure of this class
of noncompact manifolds allows to make use of calculi of pseudodifferential operators and Fourier integral operators associated with weighted symbols globally defined on ℝn. By means of these tools, we improve known results concerning the remainder terms of the Weyl Formulae for NP(λ) and show how their behaviour depends on the ratio m/μ and the dimension of M. |
| format | Article |
| id | doaj-art-d1efb083f85049e0a1d4ec3323e9a131 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d1efb083f85049e0a1d4ec3323e9a1312025-02-03T01:12:03ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/909782909782On the Spectral Asymptotics of Operators on Manifolds with EndsSandro Coriasco0Lidia Maniccia1Dipartimento di Matematica, Università degli Studi di Torino, V. C. Alberto, n. 10, I-10123 Torino, ItalyDipartimento di Matematica, Università degli Studi di Torino, V. C. Alberto, n. 10, I-10123 Torino, ItalyWe deal with the asymptotic behaviour, for λ→+∞, of the counting function NP(λ) of certain positive self-adjoint operators P with double order (m,μ), m,μ > 0, m≠μ , defined on a manifold with ends M. The structure of this class of noncompact manifolds allows to make use of calculi of pseudodifferential operators and Fourier integral operators associated with weighted symbols globally defined on ℝn. By means of these tools, we improve known results concerning the remainder terms of the Weyl Formulae for NP(λ) and show how their behaviour depends on the ratio m/μ and the dimension of M.http://dx.doi.org/10.1155/2013/909782 |
| spellingShingle | Sandro Coriasco Lidia Maniccia On the Spectral Asymptotics of Operators on Manifolds with Ends Abstract and Applied Analysis |
| title | On the Spectral Asymptotics of Operators on Manifolds with Ends |
| title_full | On the Spectral Asymptotics of Operators on Manifolds with Ends |
| title_fullStr | On the Spectral Asymptotics of Operators on Manifolds with Ends |
| title_full_unstemmed | On the Spectral Asymptotics of Operators on Manifolds with Ends |
| title_short | On the Spectral Asymptotics of Operators on Manifolds with Ends |
| title_sort | on the spectral asymptotics of operators on manifolds with ends |
| url | http://dx.doi.org/10.1155/2013/909782 |
| work_keys_str_mv | AT sandrocoriasco onthespectralasymptoticsofoperatorsonmanifoldswithends AT lidiamaniccia onthespectralasymptoticsofoperatorsonmanifoldswithends |