The Almost Everywhere Convergence of Eigenfunction Expansions of Schrödinger Operator in Lp Classes
In this paper the eigenfunction expansions of the Schrödinger operator with the potential having singularity at one point are considered. The uniform estimations for the spectral function of the Schrödinger operator in closed domain are obtained. The almost everywhere convergence of the eigenfunctio...
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| Format: | Article |
| Language: | English English |
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Universiti Putra Malaysia
2017
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| Online Access: | http://umpir.ump.edu.my/id/eprint/18819/1/The%20Almost%20Everywhere%20Convergence%20of%20Eigenfunction%20Expansions%20of%20Schr%C3%B6dinger%20Operator%20in%20Lp%20Classes.pdf http://umpir.ump.edu.my/id/eprint/18819/2/The%20Almost%20Everywhere%20Convergence%20of%20Eigenfunction%20Expansions%20of%20Schr%C3%B6dinger%20Operator%20in%20Lp%20Classes%201.pdf |
| _version_ | 1825823935462113280 |
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| author | N. A., Jamaludin Ahmedov, Anvarjon A. |
| author_facet | N. A., Jamaludin Ahmedov, Anvarjon A. |
| author_sort | N. A., Jamaludin |
| collection | UMP |
| description | In this paper the eigenfunction expansions of the Schrödinger operator with the potential having singularity at one point are considered. The uniform estimations for the spectral function of the Schrödinger operator in closed domain are obtained. The almost everywhere convergence of the eigenfunction expansions by Riesz means in the classes Lp classes is proven by estimating the maximal operator in L1 and L2 and applying the interpolation theorem for the family of linear operators.
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| first_indexed | 2024-03-06T12:18:30Z |
| format | Article |
| id | UMPir18819 |
| institution | Universiti Malaysia Pahang |
| language | English English |
| last_indexed | 2024-03-06T12:18:30Z |
| publishDate | 2017 |
| publisher | Universiti Putra Malaysia |
| record_format | dspace |
| spelling | UMPir188192018-05-02T06:37:38Z http://umpir.ump.edu.my/id/eprint/18819/ The Almost Everywhere Convergence of Eigenfunction Expansions of Schrödinger Operator in Lp Classes N. A., Jamaludin Ahmedov, Anvarjon A. Q Science (General) In this paper the eigenfunction expansions of the Schrödinger operator with the potential having singularity at one point are considered. The uniform estimations for the spectral function of the Schrödinger operator in closed domain are obtained. The almost everywhere convergence of the eigenfunction expansions by Riesz means in the classes Lp classes is proven by estimating the maximal operator in L1 and L2 and applying the interpolation theorem for the family of linear operators. Universiti Putra Malaysia 2017 Article PeerReviewed application/pdf en http://umpir.ump.edu.my/id/eprint/18819/1/The%20Almost%20Everywhere%20Convergence%20of%20Eigenfunction%20Expansions%20of%20Schr%C3%B6dinger%20Operator%20in%20Lp%20Classes.pdf application/pdf en http://umpir.ump.edu.my/id/eprint/18819/2/The%20Almost%20Everywhere%20Convergence%20of%20Eigenfunction%20Expansions%20of%20Schr%C3%B6dinger%20Operator%20in%20Lp%20Classes%201.pdf N. A., Jamaludin and Ahmedov, Anvarjon A. (2017) The Almost Everywhere Convergence of Eigenfunction Expansions of Schrödinger Operator in Lp Classes. Malaysian Journal of Mathematical Sciences, 11 (S2). pp. 119-136. ISSN 18238343. (Published) http://einspem.upm.edu.my/journal/fullpaper/vol11sapril/10.%20Nuramalina.pdf |
| spellingShingle | Q Science (General) N. A., Jamaludin Ahmedov, Anvarjon A. The Almost Everywhere Convergence of Eigenfunction Expansions of Schrödinger Operator in Lp Classes |
| title | The Almost Everywhere Convergence of Eigenfunction Expansions of Schrödinger Operator in Lp Classes |
| title_full | The Almost Everywhere Convergence of Eigenfunction Expansions of Schrödinger Operator in Lp Classes |
| title_fullStr | The Almost Everywhere Convergence of Eigenfunction Expansions of Schrödinger Operator in Lp Classes |
| title_full_unstemmed | The Almost Everywhere Convergence of Eigenfunction Expansions of Schrödinger Operator in Lp Classes |
| title_short | The Almost Everywhere Convergence of Eigenfunction Expansions of Schrödinger Operator in Lp Classes |
| title_sort | almost everywhere convergence of eigenfunction expansions of schrodinger operator in lp classes |
| topic | Q Science (General) |
| url | http://umpir.ump.edu.my/id/eprint/18819/1/The%20Almost%20Everywhere%20Convergence%20of%20Eigenfunction%20Expansions%20of%20Schr%C3%B6dinger%20Operator%20in%20Lp%20Classes.pdf http://umpir.ump.edu.my/id/eprint/18819/2/The%20Almost%20Everywhere%20Convergence%20of%20Eigenfunction%20Expansions%20of%20Schr%C3%B6dinger%20Operator%20in%20Lp%20Classes%201.pdf |
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