A modified \(P\)-adic integral and a modified \(P\)-adic derivative for functions defined on a half-axis (Q881231)
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scientific article; zbMATH DE number 5155798
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A modified \(P\)-adic integral and a modified \(P\)-adic derivative for functions defined on a half-axis |
scientific article; zbMATH DE number 5155798 |
Statements
A modified \(P\)-adic integral and a modified \(P\)-adic derivative for functions defined on a half-axis (English)
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22 May 2007
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The author introduces a generalized Fourier-Walsh transform replacing dyadic decomposition by \(P\)-adic decomposition, where \(P\) is a fixed symmetric subset of \(\mathbb{Z}\). Generalizing the known results for Fourier-Walsh transform he proves several theorems on properties of \(P\)-adic integrals and derivatives and establishes a Hardy type inequality for \(P\)-adic Fourier-Walsh transform.
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\(P\)-adic Fourier-Walsh transform
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\(P\)-adic integral
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\(P\)-adic derivative
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Hardy inequality
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