Summability methods based on the Riemann Zeta function
This paper is a study of summability methods that are based on the Riemann Zeta function. A limitation theorem is proved which gives a necessary condition for a sequence x to be zeta summable. A zeta summability matrix Zt associated with a real sequence t is introduced; a necessary and sufficient co...
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| Format: | Article |
| Language: | English |
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Wiley
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171288000067 |
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| _version_ | 1832556283958394880 |
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| author | Larry K. Chu |
| author_facet | Larry K. Chu |
| author_sort | Larry K. Chu |
| collection | DOAJ |
| description | This paper is a study of summability methods that are based on the Riemann Zeta function. A limitation theorem is proved which gives a necessary condition for a sequence x to be zeta summable. A zeta summability matrix Zt associated with a real sequence t is introduced; a necessary and sufficient condition on the sequence t such that Zt maps l1 to l1 is established. Results comparing the strength of the zeta method to that of well-known summability methods are also investigated. |
| format | Article |
| id | doaj-art-96d27937224f4d189652597c1b574b77 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1988-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-96d27937224f4d189652597c1b574b772025-02-03T05:45:53ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251988-01-01111273610.1155/S0161171288000067Summability methods based on the Riemann Zeta functionLarry K. Chu0Department of Mathematics and Computer Science, State University Of North Dakota - Minot, Minot 58701, ND, USAThis paper is a study of summability methods that are based on the Riemann Zeta function. A limitation theorem is proved which gives a necessary condition for a sequence x to be zeta summable. A zeta summability matrix Zt associated with a real sequence t is introduced; a necessary and sufficient condition on the sequence t such that Zt maps l1 to l1 is established. Results comparing the strength of the zeta method to that of well-known summability methods are also investigated.http://dx.doi.org/10.1155/S0161171288000067zeta summability methodzeta matrix methodl−l matrixCesaro methodEuler-Knopp method. |
| spellingShingle | Larry K. Chu Summability methods based on the Riemann Zeta function International Journal of Mathematics and Mathematical Sciences zeta summability method zeta matrix method l−l matrix Cesaro method Euler-Knopp method. |
| title | Summability methods based on the Riemann Zeta function |
| title_full | Summability methods based on the Riemann Zeta function |
| title_fullStr | Summability methods based on the Riemann Zeta function |
| title_full_unstemmed | Summability methods based on the Riemann Zeta function |
| title_short | Summability methods based on the Riemann Zeta function |
| title_sort | summability methods based on the riemann zeta function |
| topic | zeta summability method zeta matrix method l−l matrix Cesaro method Euler-Knopp method. |
| url | http://dx.doi.org/10.1155/S0161171288000067 |
| work_keys_str_mv | AT larrykchu summabilitymethodsbasedontheriemannzetafunction |