On Changes of Variable Preserving the Convergence and Absolute Convergence of Fourier Series in the Haar Wavelet System
| Autor: | K. R. Bitsadze |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
General Mathematics
010102 general mathematics Convergence of Fourier series 02 engineering and technology Absolute convergence 01 natural sciences Haar wavelet 020303 mechanical engineering & transports 0203 mechanical engineering Integer Convergence (routing) Applied mathematics 0101 mathematics Fourier series Mathematics Variable (mathematics) |
| Zdroj: | Mathematical Notes. 108:162-170 |
| ISSN: | 1573-8876 0001-4346 |
| DOI: | 10.1134/s0001434620070172 |
| Popis: | It is established that, among all continuously differentiable homeomorphic changes of variable, the absolute convergence of Fourier series in the Haar wavelet system is preserved by only those for which $$\varphi^{-1}(0)$$ is binary-rational and $$\varphi'(x)=\pm 2^m$$ , where $$m$$ is an integer and $$x\in\mathbb R$$ . It is also established that this condition is necessary for a continuously differentiable homeomorphic change of variable to preserve the convergence of Fourier series in the Haar wavelet system. |
| Databáze: | OpenAIRE |
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