Year: 2019
Type: preprint
Abstract: This work characterizes (dyadic) wavelet frames for $L^2({\mathbb R})$ by means of spectral techniques. These techniques use decomposability properties of the frame operator in spectral representations associated to the dilation operator. The approach is closely related to usual Fourier domain fiberization techniques, dual Gramian analysis and extension principles, which are described here on the basis of the periodized Fourier transform. In a second paper of this series, we shall show how the spectral formulas obtained here permit us to calculate all the tight wavelet frames for $L^2({\mathbb R})$ with a fixed number of generators of minimal support.
Source: arXiv (Cornell University)
Authors: Gómez-Cubillo, F., Villullas, S.
Institutions: Universidad de Valladolid, Universidad Carlos III de Madrid
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2914336505