On Generalized Localization of Fourier Inversion Associated with an Elliptic Operator for Distributions
We study the behavior of Fourier integrals summed by the symbols of elliptic operators and pointwise convergence of Fourier inversion. We consider generalized localization principle which in classical Lp spaces was investigated by Sjölin (1983), Carbery and Soria (1988, 1997) and Alimov (1993). Proc...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/649848 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832561324411846656 |
|---|---|
| author | Ravshan Ashurov Almaz Butaev Biswajeet Pradhan |
| author_facet | Ravshan Ashurov Almaz Butaev Biswajeet Pradhan |
| author_sort | Ravshan Ashurov |
| collection | DOAJ |
| description | We study the behavior of Fourier integrals summed by the symbols of elliptic operators and pointwise convergence of Fourier inversion. We consider generalized localization principle which in classical Lp spaces was investigated by Sjölin (1983), Carbery and Soria (1988, 1997) and Alimov (1993). Proceeding these studies, in this paper, we establish sharp conditions for generalized localization in the class of finitely supported distributions. |
| format | Article |
| id | doaj-art-dede2ed6de2742b99c3f154c6157ceb1 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-dede2ed6de2742b99c3f154c6157ceb12025-02-03T01:25:30ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/649848649848On Generalized Localization of Fourier Inversion Associated with an Elliptic Operator for DistributionsRavshan Ashurov0Almaz Butaev1Biswajeet Pradhan2Institute of Mathematics, National University of Uzbekistan, Hodjaeva Street 29, Tashkent 100125, UzbekistanInstitute of Advanced Technology (ITMA), University Putra Malaysia, 43400 Serdang, Selangor, MalaysiaInstitute of Advanced Technology (ITMA), University Putra Malaysia, 43400 Serdang, Selangor, MalaysiaWe study the behavior of Fourier integrals summed by the symbols of elliptic operators and pointwise convergence of Fourier inversion. We consider generalized localization principle which in classical Lp spaces was investigated by Sjölin (1983), Carbery and Soria (1988, 1997) and Alimov (1993). Proceeding these studies, in this paper, we establish sharp conditions for generalized localization in the class of finitely supported distributions.http://dx.doi.org/10.1155/2012/649848 |
| spellingShingle | Ravshan Ashurov Almaz Butaev Biswajeet Pradhan On Generalized Localization of Fourier Inversion Associated with an Elliptic Operator for Distributions Abstract and Applied Analysis |
| title | On Generalized Localization of Fourier Inversion Associated with an Elliptic Operator for Distributions |
| title_full | On Generalized Localization of Fourier Inversion Associated with an Elliptic Operator for Distributions |
| title_fullStr | On Generalized Localization of Fourier Inversion Associated with an Elliptic Operator for Distributions |
| title_full_unstemmed | On Generalized Localization of Fourier Inversion Associated with an Elliptic Operator for Distributions |
| title_short | On Generalized Localization of Fourier Inversion Associated with an Elliptic Operator for Distributions |
| title_sort | on generalized localization of fourier inversion associated with an elliptic operator for distributions |
| url | http://dx.doi.org/10.1155/2012/649848 |
| work_keys_str_mv | AT ravshanashurov ongeneralizedlocalizationoffourierinversionassociatedwithanellipticoperatorfordistributions AT almazbutaev ongeneralizedlocalizationoffourierinversionassociatedwithanellipticoperatorfordistributions AT biswajeetpradhan ongeneralizedlocalizationoffourierinversionassociatedwithanellipticoperatorfordistributions |