On nonspherical partial sums of fourier integrals of continuous functions from the Sobolev spaces
The partial integrals of the N-fold Fourier integrals connected with elliptic polynomials (not necessarily homogeneous; principal part of which has a strictly convex level surface) are considered. It is proved that if a + s > (N – 1)/2 and ap = N then the Riesz means of the nonnegati...
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| Format: | Article |
| Language: | English |
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Universiti Putra Malaysia Press
2011
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| Online Access: | http://psasir.upm.edu.my/id/eprint/40412/ http://psasir.upm.edu.my/id/eprint/40412/1/On%20Nonspherical%20Partial%20Sums%20of%20Fourier%20Integrals%20of%20Continuous.pdf |
| _version_ | 1848849417748086784 |
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| author | Ashurov, Ravshan |
| author_facet | Ashurov, Ravshan |
| author_sort | Ashurov, Ravshan |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The partial integrals of the N-fold Fourier integrals connected with elliptic polynomials (not necessarily homogeneous; principal part of which has a strictly convex level surface) are considered. It is proved that if a + s > (N – 1)/2 and ap = N then the Riesz means of the nonnegative orders of the N-fold Fourier integrals of continuous finite functions from the Sobolev spaces Wpa(RN) converge uniformly on every compact set, and if a + s > (N – 1)/2 and ap = N, then for any x0∈ RN there exists a continuous finite function from the Sobolev space such, that the corresponding Riesz means of the N-fold Fourier integrals diverge to infinity at x0. AMS
2000 Mathematics Subject Classifications: Primary 42B08; Secondary 42C14 |
| first_indexed | 2025-11-15T09:50:04Z |
| format | Article |
| id | upm-40412 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:50:04Z |
| publishDate | 2011 |
| publisher | Universiti Putra Malaysia Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-404122015-11-18T05:57:15Z http://psasir.upm.edu.my/id/eprint/40412/ On nonspherical partial sums of fourier integrals of continuous functions from the Sobolev spaces Ashurov, Ravshan The partial integrals of the N-fold Fourier integrals connected with elliptic polynomials (not necessarily homogeneous; principal part of which has a strictly convex level surface) are considered. It is proved that if a + s > (N – 1)/2 and ap = N then the Riesz means of the nonnegative orders of the N-fold Fourier integrals of continuous finite functions from the Sobolev spaces Wpa(RN) converge uniformly on every compact set, and if a + s > (N – 1)/2 and ap = N, then for any x0∈ RN there exists a continuous finite function from the Sobolev space such, that the corresponding Riesz means of the N-fold Fourier integrals diverge to infinity at x0. AMS 2000 Mathematics Subject Classifications: Primary 42B08; Secondary 42C14 Universiti Putra Malaysia Press 2011 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/40412/1/On%20Nonspherical%20Partial%20Sums%20of%20Fourier%20Integrals%20of%20Continuous.pdf Ashurov, Ravshan (2011) On nonspherical partial sums of fourier integrals of continuous functions from the Sobolev spaces. Pertanika Journal of Science & Technology, 19 (S). pp. 11-14. ISSN 0128-7680; ESSN: 2231-8526 http://www.pertanika.upm.edu.my/Pertanika%20PAPERS/JST%20Vol.%2019%20%28S%29%20Oct.%202011/07%20Pg%2011-14.pdf |
| spellingShingle | Ashurov, Ravshan On nonspherical partial sums of fourier integrals of continuous functions from the Sobolev spaces |
| title | On nonspherical partial sums of fourier integrals of continuous functions from the Sobolev spaces |
| title_full | On nonspherical partial sums of fourier integrals of continuous functions from the Sobolev spaces |
| title_fullStr | On nonspherical partial sums of fourier integrals of continuous functions from the Sobolev spaces |
| title_full_unstemmed | On nonspherical partial sums of fourier integrals of continuous functions from the Sobolev spaces |
| title_short | On nonspherical partial sums of fourier integrals of continuous functions from the Sobolev spaces |
| title_sort | on nonspherical partial sums of fourier integrals of continuous functions from the sobolev spaces |
| url | http://psasir.upm.edu.my/id/eprint/40412/ http://psasir.upm.edu.my/id/eprint/40412/ http://psasir.upm.edu.my/id/eprint/40412/1/On%20Nonspherical%20Partial%20Sums%20of%20Fourier%20Integrals%20of%20Continuous.pdf |