The Abel-type transformations into ℓ
Let t be a sequence in (0,1) that converges to 1, and define the Abel-type matrix Aα,t by ank=(k+α k)tnk+1(1−tn)α+1 for α>−1. The matrix Aα,t determines a sequence-to-sequence variant of the Abel-type power series method of summability introduced by Borwein in [1]. The purpose of this paper i...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1999-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171299227755 |
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| Summary: | Let t be a sequence in (0,1) that converges to 1, and define the Abel-type matrix Aα,t by ank=(k+α k)tnk+1(1−tn)α+1 for α>−1. The matrix Aα,t determines a sequence-to-sequence variant of the Abel-type power series method of summability introduced by Borwein in [1]. The purpose of
this paper is to study these matrices as mappings into ℓ.
Necessary and sufficient conditions for Aα,t to be ℓ-ℓ,G-ℓ, and Gw-ℓ are established. Also, the strength of Aα,t in the ℓ-ℓ setting is investigated. |
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| ISSN: | 0161-1712 1687-0425 |