On the regularizations Fourier series of distributions
Fourier analysis has many applications in various science and technology. In most problem researchers have to analyze functions (data), which has some singularities. This makes some difficulties in Fourier analysis of singular functional. In these, harmonic analysis in the spaces of distributions ca...
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| Format: | Conference or Workshop Item |
| Language: | English |
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IEEE
2011
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| Online Access: | http://psasir.upm.edu.my/id/eprint/45579/1/On%20the%20regularizations%20Fourier%20series%20of%20distributions.pdf |
| _version_ | 1796974561374240768 |
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| author | Rakhimov, Abdumalik |
| author_facet | Rakhimov, Abdumalik |
| author_sort | Rakhimov, Abdumalik |
| collection | UPM |
| description | Fourier analysis has many applications in various science and technology. In most problem researchers have to analyze functions (data), which has some singularities. This makes some difficulties in Fourier analysis of singular functional. In these, harmonic analysis in the spaces of distributions can be applied.
Recently (see for instance [9]-[11]) interest in spectral expansions of distributions increased and number of research papers were published. Present work it devoted to convergence/summation and regularization of Fourier series of distributions in different topologies.
In multidimensional case, convergence essentially depends on methods of summation, i.e. on the definition of partial sums. Even “good” defined partial sums may not supply convergence of Fourier series and in this case, some regularization of the partial sums is required. |
| first_indexed | 2024-03-06T08:58:50Z |
| format | Conference or Workshop Item |
| id | upm.eprints-45579 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:58:50Z |
| publishDate | 2011 |
| publisher | IEEE |
| record_format | dspace |
| spelling | upm.eprints-455792020-08-07T02:25:37Z http://psasir.upm.edu.my/id/eprint/45579/ On the regularizations Fourier series of distributions Rakhimov, Abdumalik Fourier analysis has many applications in various science and technology. In most problem researchers have to analyze functions (data), which has some singularities. This makes some difficulties in Fourier analysis of singular functional. In these, harmonic analysis in the spaces of distributions can be applied. Recently (see for instance [9]-[11]) interest in spectral expansions of distributions increased and number of research papers were published. Present work it devoted to convergence/summation and regularization of Fourier series of distributions in different topologies. In multidimensional case, convergence essentially depends on methods of summation, i.e. on the definition of partial sums. Even “good” defined partial sums may not supply convergence of Fourier series and in this case, some regularization of the partial sums is required. IEEE 2011 Conference or Workshop Item PeerReviewed text en http://psasir.upm.edu.my/id/eprint/45579/1/On%20the%20regularizations%20Fourier%20series%20of%20distributions.pdf Rakhimov, Abdumalik (2011) On the regularizations Fourier series of distributions. In: 4th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO 2011), 19-21 Apr. 2011, Kuala Lumpur, Malaysia. . 10.1109/ICMSAO.2011.5775632 |
| spellingShingle | Rakhimov, Abdumalik On the regularizations Fourier series of distributions |
| title | On the regularizations Fourier series of distributions |
| title_full | On the regularizations Fourier series of distributions |
| title_fullStr | On the regularizations Fourier series of distributions |
| title_full_unstemmed | On the regularizations Fourier series of distributions |
| title_short | On the regularizations Fourier series of distributions |
| title_sort | on the regularizations fourier series of distributions |
| url | http://psasir.upm.edu.my/id/eprint/45579/1/On%20the%20regularizations%20Fourier%20series%20of%20distributions.pdf |
| work_keys_str_mv | AT rakhimovabdumalik ontheregularizationsfourierseriesofdistributions |