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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.01399 |
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| _version_ | 1866916877940293632 |
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| author | Davydov, Oleg Tushev, Anatolii |
| author_facet | Davydov, Oleg Tushev, Anatolii |
| contents | We suggest a new method of basis construction for the kernel of a linear form on the Laurent polynomial module related to multivariate wavelets, and demonstrate its applications to box spline prewavelets, leading to small mask supports for $C^1$ cubic and $C^2$ quartic box splines in two variables, outperforming previously known constructions, and to trivariate piecewise linear prewavelets with at most 23 nozero mask coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01399 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Construction of Bases in Modules over Laurent Polynomial Rings and Applications to Box Spline Prewavelets Davydov, Oleg Tushev, Anatolii Numerical Analysis Commutative Algebra 42C40, 65T60, 13C10 We suggest a new method of basis construction for the kernel of a linear form on the Laurent polynomial module related to multivariate wavelets, and demonstrate its applications to box spline prewavelets, leading to small mask supports for $C^1$ cubic and $C^2$ quartic box splines in two variables, outperforming previously known constructions, and to trivariate piecewise linear prewavelets with at most 23 nozero mask coefficients. |
| title | Construction of Bases in Modules over Laurent Polynomial Rings and Applications to Box Spline Prewavelets |
| topic | Numerical Analysis Commutative Algebra 42C40, 65T60, 13C10 |
| url | https://arxiv.org/abs/2508.01399 |