On the space \(\ell^p(\beta)\) (Q1567578)
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scientific article; zbMATH DE number 1462209
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the space \(\ell^p(\beta)\) |
scientific article; zbMATH DE number 1462209 |
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On the space \(\ell^p(\beta)\) (English)
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15 January 2001
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Given a sequence \((\beta_n)_n\) of positive weights, the author studies the Banach space \(\ell^p(\beta)\) of all power series \(f(z)= \sum^\infty_{n=0} \widehat f(n)z^n\) for which the norm \[ \|f\|:= \Biggl(\sum^\infty_{n= 0}|\widehat f(n)|^p \beta^p_n\Biggr)^{1/p} \] makes sense and is finite.
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power series space
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positive weights
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