Localization and summability of multiple Hermite series
The multiple Hermite series in Rn are investigated by the Riesz summability method of order α>(n−1)/2. More precisely, localization theorems for some classes of functions are proved and sharp sufficient conditions are given. Thus the classical Szegö results are extended to the n-dimensional case....
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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171297000100 |
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| _version_ | 1832545333104607232 |
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| author | G. E. Karadzhov E. E. El-Adad |
| author_facet | G. E. Karadzhov E. E. El-Adad |
| author_sort | G. E. Karadzhov |
| collection | DOAJ |
| description | The multiple Hermite series in Rn are investigated by the Riesz summability
method of order α>(n−1)/2. More precisely, localization theorems for some classes of functions
are proved and sharp sufficient conditions are given. Thus the classical Szegö results are extended
to the n-dimensional case. In particular, for these classes of functions the localization principle
and summability on the Lebesgue set are established. |
| format | Article |
| id | doaj-art-cb2d674ce7f64d5ea05e0a12191ec44c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-cb2d674ce7f64d5ea05e0a12191ec44c2025-02-03T07:26:10ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-01201617410.1155/S0161171297000100Localization and summability of multiple Hermite seriesG. E. Karadzhov0E. E. El-Adad1Institute of Mathematics, Bulgarian Academy of Sciences, Sofia 1113, BulgariaInstitute of Mathematics, Bulgarian Academy of Sciences, Sofia 1113, BulgariaThe multiple Hermite series in Rn are investigated by the Riesz summability method of order α>(n−1)/2. More precisely, localization theorems for some classes of functions are proved and sharp sufficient conditions are given. Thus the classical Szegö results are extended to the n-dimensional case. In particular, for these classes of functions the localization principle and summability on the Lebesgue set are established.http://dx.doi.org/10.1155/S0161171297000100Riesz summabilitymultiple Hermite series. |
| spellingShingle | G. E. Karadzhov E. E. El-Adad Localization and summability of multiple Hermite series International Journal of Mathematics and Mathematical Sciences Riesz summability multiple Hermite series. |
| title | Localization and summability of multiple Hermite series |
| title_full | Localization and summability of multiple Hermite series |
| title_fullStr | Localization and summability of multiple Hermite series |
| title_full_unstemmed | Localization and summability of multiple Hermite series |
| title_short | Localization and summability of multiple Hermite series |
| title_sort | localization and summability of multiple hermite series |
| topic | Riesz summability multiple Hermite series. |
| url | http://dx.doi.org/10.1155/S0161171297000100 |
| work_keys_str_mv | AT gekaradzhov localizationandsummabilityofmultiplehermiteseries AT eeeladad localizationandsummabilityofmultiplehermiteseries |