Rational Orthonormal Littlewood-Paley Wavelet Basis of L2(R)
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917075789807616 |
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| author | Sun, Changping |
| author_facet | Sun, Changping |
| contents | In this letter, first, we prove that the orthonormal basis of rational Littlewood-Paley wavelet with rational dilation factor M=p/q first proposed by Auscher does not hold for all rational numbers. It does not hold if q is not equal to 1. In other words, it is not an orthonormal basis if the rational dilation factor M is not an integer. Then, to make up for the shortcoming of the rational Littlewood-Paley wavelet proposed by Auscher, a new orthonormal basis of rational Littlewood-Paley wavelet with rational dilation factor M=p/q is proposed, which holds for all rational numbers. Finally, by means of sampling theorem for bandpass signals, it is proved completely that the new rational Littlewood-Paley wavelet family is an orthonormal wavelet basis of L2(R). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08984 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rational Orthonormal Littlewood-Paley Wavelet Basis of L2(R) Sun, Changping Functional Analysis In this letter, first, we prove that the orthonormal basis of rational Littlewood-Paley wavelet with rational dilation factor M=p/q first proposed by Auscher does not hold for all rational numbers. It does not hold if q is not equal to 1. In other words, it is not an orthonormal basis if the rational dilation factor M is not an integer. Then, to make up for the shortcoming of the rational Littlewood-Paley wavelet proposed by Auscher, a new orthonormal basis of rational Littlewood-Paley wavelet with rational dilation factor M=p/q is proposed, which holds for all rational numbers. Finally, by means of sampling theorem for bandpass signals, it is proved completely that the new rational Littlewood-Paley wavelet family is an orthonormal wavelet basis of L2(R). |
| title | Rational Orthonormal Littlewood-Paley Wavelet Basis of L2(R) |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2511.08984 |