Some Sharp L^2 Inequalities for Dirac Type Operators
We use the spectra of Dirac type operators on the sphere $S^n$ to produce sharp $L^2$ inequalities on the sphere. These operators include the Dirac operator on $S^n$, the conformal Laplacian and Paenitz operator. We use the Cayley transform, or stereographic projection, to obtain similar inequalitie...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2007-11-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://www.emis.de/journals/SIGMA/2007/114/ |
| _version_ | 1818209311734628352 |
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| author | Alexander Balinsky John Ryan |
| author_facet | Alexander Balinsky John Ryan |
| author_sort | Alexander Balinsky |
| collection | DOAJ |
| description | We use the spectra of Dirac type operators on the sphere $S^n$ to produce sharp $L^2$ inequalities on the sphere. These operators include the Dirac operator on $S^n$, the conformal Laplacian and Paenitz operator. We use the Cayley transform, or stereographic projection, to obtain similar inequalities for powers of the Dirac operator and their inverses in ${mathbb R}^n$. |
| first_indexed | 2024-12-12T04:58:42Z |
| format | Article |
| id | doaj.art-856fad339aef4064a302a748ac9eb72c |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-12T04:58:42Z |
| publishDate | 2007-11-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-856fad339aef4064a302a748ac9eb72c2022-12-22T00:37:17ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592007-11-013114Some Sharp L^2 Inequalities for Dirac Type OperatorsAlexander BalinskyJohn RyanWe use the spectra of Dirac type operators on the sphere $S^n$ to produce sharp $L^2$ inequalities on the sphere. These operators include the Dirac operator on $S^n$, the conformal Laplacian and Paenitz operator. We use the Cayley transform, or stereographic projection, to obtain similar inequalities for powers of the Dirac operator and their inverses in ${mathbb R}^n$.http://www.emis.de/journals/SIGMA/2007/114/Dirac operatorClifford algebraconformal LaplacianPaenitz operator |
| spellingShingle | Alexander Balinsky John Ryan Some Sharp L^2 Inequalities for Dirac Type Operators Symmetry, Integrability and Geometry: Methods and Applications Dirac operator Clifford algebra conformal Laplacian Paenitz operator |
| title | Some Sharp L^2 Inequalities for Dirac Type Operators |
| title_full | Some Sharp L^2 Inequalities for Dirac Type Operators |
| title_fullStr | Some Sharp L^2 Inequalities for Dirac Type Operators |
| title_full_unstemmed | Some Sharp L^2 Inequalities for Dirac Type Operators |
| title_short | Some Sharp L^2 Inequalities for Dirac Type Operators |
| title_sort | some sharp l 2 inequalities for dirac type operators |
| topic | Dirac operator Clifford algebra conformal Laplacian Paenitz operator |
| url | http://www.emis.de/journals/SIGMA/2007/114/ |
| work_keys_str_mv | AT alexanderbalinsky somesharpl2inequalitiesfordiractypeoperators AT johnryan somesharpl2inequalitiesfordiractypeoperators |