Some Tauberian theorems for Euler and Borel summability
The well-known summability methods of Euler and Borel are studied as mappings from ℓ1 into ℓ1. In this ℓ−ℓ setting, the following Tauberian results are proved: if x is a sequence that is mapped into ℓ1 by the Euler-Knopp method Er with r>0 (or the Borel matrix method) and x satisfies ∑n=0∞|xn−xn+...
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| Format: | Article |
| Language: | English |
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Wiley
1980-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171280000531 |
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| _version_ | 1849435001692618752 |
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| author | J. A. Fridy K. L. Roberts |
| author_facet | J. A. Fridy K. L. Roberts |
| author_sort | J. A. Fridy |
| collection | DOAJ |
| description | The well-known summability methods of Euler and Borel are studied as mappings from ℓ1 into ℓ1. In this ℓ−ℓ setting, the following Tauberian results are proved: if x is a sequence that is mapped into ℓ1 by the Euler-Knopp method Er with r>0 (or the Borel matrix method) and x satisfies ∑n=0∞|xn−xn+1|n<∞, then x itself is in ℓ1. |
| format | Article |
| id | doaj-art-e4b29bea9c1144e2baa733cbf6b7c85a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1980-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e4b29bea9c1144e2baa733cbf6b7c85a2025-08-20T03:26:26ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251980-01-013473173810.1155/S0161171280000531Some Tauberian theorems for Euler and Borel summabilityJ. A. Fridy0K. L. Roberts1Department of Mathematics, Kent State University, Kent 44252, Ohio, USADepartment of Mathematics, The University of Western Ontario, Ontario, London, CanadaThe well-known summability methods of Euler and Borel are studied as mappings from ℓ1 into ℓ1. In this ℓ−ℓ setting, the following Tauberian results are proved: if x is a sequence that is mapped into ℓ1 by the Euler-Knopp method Er with r>0 (or the Borel matrix method) and x satisfies ∑n=0∞|xn−xn+1|n<∞, then x itself is in ℓ1.http://dx.doi.org/10.1155/S0161171280000531Tauberian conditionℓ−ℓ methodEular-Knopp meansBorel exponential method. |
| spellingShingle | J. A. Fridy K. L. Roberts Some Tauberian theorems for Euler and Borel summability International Journal of Mathematics and Mathematical Sciences Tauberian condition ℓ−ℓ method Eular-Knopp means Borel exponential method. |
| title | Some Tauberian theorems for Euler and Borel summability |
| title_full | Some Tauberian theorems for Euler and Borel summability |
| title_fullStr | Some Tauberian theorems for Euler and Borel summability |
| title_full_unstemmed | Some Tauberian theorems for Euler and Borel summability |
| title_short | Some Tauberian theorems for Euler and Borel summability |
| title_sort | some tauberian theorems for euler and borel summability |
| topic | Tauberian condition ℓ−ℓ method Eular-Knopp means Borel exponential method. |
| url | http://dx.doi.org/10.1155/S0161171280000531 |
| work_keys_str_mv | AT jafridy sometauberiantheoremsforeulerandborelsummability AT klroberts sometauberiantheoremsforeulerandborelsummability |