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Dilation equations and the smoothness of compactly supported wavelets
| Content Provider | Scilit |
|---|---|
| Author | Heil, Christopher Colella, David |
| Copyright Year | 2021 |
| Description | The construction of compactly supported wavelets with specified amounts of smoothness is an important problem in wavelet theory. This problem reduces to the construction of scaling functions, i.e., solutions f of dilation equations f ( t ) = ∑ k = 0 N c k f ( 2 t – k ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003210450/ad6c41bf-0278-4d2b-bb3c-857b8602ed93/content/eq1959.tif"/> , with specified smoothness. This article characterizes all smooth, compactly supported scaling functions in terms of a joint spectral radius of two N × N matrices T$ _{0}$, T$ _{1}$ constructed from the coefficients {c$ _{0},…,c_{N}$ } of the dilation equation, restricted to an appropriate subspace of $ℂ^{ N }$. The number of continuous derivatives of the scaling function and the range of Hölder exponents of continuity of the last continuous derivative are determined by the value of this joint spectral radius. Numerous examples are provided to illustrate the results. Book Name: Wavelets |
| Related Links | https://api.taylorfrancis.com/content/chapters/edit/download?identifierName=doi&identifierValue=10.1201/9781003210450-5&type=chapterpdf |
| Ending Page | 201 |
| Page Count | 39 |
| Starting Page | 163 |
| DOI | 10.1201/9781003210450-5 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2021-07-07 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Wavelets Applied Mathematics Functions Wavelets Smoothness Dilation Equations Compactly Supported Construction |
| Content Type | Text |
| Resource Type | Chapter |
