Special-Affine Wavelets: Multi-Resolution Analysis and Function Approximation in L^2(R)
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912811878187008 |
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| author | Sahu, Vikash K. Lone, Waseem Z. Verma, Amit K. |
| author_facet | Sahu, Vikash K. Lone, Waseem Z. Verma, Amit K. |
| contents | The multiresolution analysis (MRA) associated with the Special affine Fourier transform (SAFT) provides a structured approach for generating orthonormal bases in \( L^2(\mathbb R) \), making it a powerful tool for advanced signal analysis. This work introduces a robust sampling theory and constructs multiresolution structures within the SAFT domain to support the formation of orthonormal bases. Motivated by the need for a sampling theorem applicable to band-limited signals in the SAFT framework, we establish a corresponding theoretical foundation. Furthermore, a method for constructing orthogonal bases in $L^2(\mathbb R)$ is proposed, and the theoretical results are demonstrated through illustrative examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09612 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Special-Affine Wavelets: Multi-Resolution Analysis and Function Approximation in L^2(R) Sahu, Vikash K. Lone, Waseem Z. Verma, Amit K. Functional Analysis 42C40, 46E30, 42A38, 44A05, 94A12 The multiresolution analysis (MRA) associated with the Special affine Fourier transform (SAFT) provides a structured approach for generating orthonormal bases in \( L^2(\mathbb R) \), making it a powerful tool for advanced signal analysis. This work introduces a robust sampling theory and constructs multiresolution structures within the SAFT domain to support the formation of orthonormal bases. Motivated by the need for a sampling theorem applicable to band-limited signals in the SAFT framework, we establish a corresponding theoretical foundation. Furthermore, a method for constructing orthogonal bases in $L^2(\mathbb R)$ is proposed, and the theoretical results are demonstrated through illustrative examples. |
| title | Special-Affine Wavelets: Multi-Resolution Analysis and Function Approximation in L^2(R) |
| topic | Functional Analysis 42C40, 46E30, 42A38, 44A05, 94A12 |
| url | https://arxiv.org/abs/2510.09612 |