Compactly supported, orthogonal, continuous piecewise polynomial multiresolution analysis
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915996420276224 |
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| author | Fernández, Lidia Geronimo, Jeffrey S. Iliev, Plamen |
| author_facet | Fernández, Lidia Geronimo, Jeffrey S. Iliev, Plamen |
| contents | We present explicit representations in terms of hypergeometric functions for the scaling functions in the $C^0$ orthogonal multiresolution analyses associated with piecewise continuous polynomials. Closed formulas for the Mellin transform of these functions as well as their Fourier transforms are derived. Some new multiresolution analyses whose scaling functions have coefficients that are rational numbers are introduced and discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02908 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compactly supported, orthogonal, continuous piecewise polynomial multiresolution analysis Fernández, Lidia Geronimo, Jeffrey S. Iliev, Plamen Classical Analysis and ODEs Numerical Analysis We present explicit representations in terms of hypergeometric functions for the scaling functions in the $C^0$ orthogonal multiresolution analyses associated with piecewise continuous polynomials. Closed formulas for the Mellin transform of these functions as well as their Fourier transforms are derived. Some new multiresolution analyses whose scaling functions have coefficients that are rational numbers are introduced and discussed. |
| title | Compactly supported, orthogonal, continuous piecewise polynomial multiresolution analysis |
| topic | Classical Analysis and ODEs Numerical Analysis |
| url | https://arxiv.org/abs/2412.02908 |