Geometric Structure in Weighted Alpert Wavelets
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908285931618304 |
|---|---|
| author | Gates, Fletcher Rodney, Scott |
| author_facet | Gates, Fletcher Rodney, Scott |
| contents | In this paper we present a number of results concerning Alpert wavelet bases for $L^2(μ)$, with $μ$ a locally finite positive Borel measure on $\mathbb{R}^n$. We show that the properties of such a basis depend on linear dependences in $L^2(μ)$ among the functions from which the wavelets are constructed; this result completes an investigation begun by Rahm, Sawyer, and Wick in arXiv:1808.01223. We also show that a Gröbner basis technique can be used to efficiently detect these dependences. Lastly we give a generalization of the Alpert basis construction, where the amount of orthogonality in the basis is allowed to vary over the dyadic grid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21046 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric Structure in Weighted Alpert Wavelets Gates, Fletcher Rodney, Scott Classical Analysis and ODEs In this paper we present a number of results concerning Alpert wavelet bases for $L^2(μ)$, with $μ$ a locally finite positive Borel measure on $\mathbb{R}^n$. We show that the properties of such a basis depend on linear dependences in $L^2(μ)$ among the functions from which the wavelets are constructed; this result completes an investigation begun by Rahm, Sawyer, and Wick in arXiv:1808.01223. We also show that a Gröbner basis technique can be used to efficiently detect these dependences. Lastly we give a generalization of the Alpert basis construction, where the amount of orthogonality in the basis is allowed to vary over the dyadic grid. |
| title | Geometric Structure in Weighted Alpert Wavelets |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2503.21046 |