On the structure of the class \(A(\varphi )\) (Q881095)
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scientific article; zbMATH DE number 5155525
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the structure of the class \(A(\varphi )\) |
scientific article; zbMATH DE number 5155525 |
Statements
On the structure of the class \(A(\varphi )\) (English)
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21 May 2007
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Let \(\{\varphi_n\}\) be an orthonormal and complete system in \(L_2(0,1)\) and denote by \(A(\varphi)\) the class of functions \(f\) with absolutely convergent Fourier series: \(f(x)=\sum c_n(f) \varphi_n(x)\), \(c_n(f)=\int_0^1 f(x)\varphi_n(x)\,dx\). The author gives a necessary and sufficient condition on the system \(\{\varphi_n\}\) in order \(A(\varphi)\) to be closed under multiplication.
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Banach space
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Khinchine's inequality
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Rademacher function
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Haar system
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Walsh system
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Fourier coefficients
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0.91585666
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0.8695468
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