<abstract xmlns="http://www.w3.org/1999/xhtml"><p>A generalization of Mallat’s classic theory of multiresolution analysis based on the theory of spectral pairs was considered by <xref ref-type="bibr" rid="j_ausm-2018-0026_ref_004_w2aab3b7b9b1b6b1ab1ab4Aa">Gabardo and Nashed [4]</xref> for which the translation set Λ = {0, r/N}+2 ℤ is no longer a discrete subgroup of ℝ but a spectrum associated with a certain one-dimensional spectral pair. In this short communication, we characterize the scaling functions associated with such a nonuniform multiresolution analysis by means of some fundamental equations in the Fourier domain.</p></abstract>

A generalization of Mallat’s classic theory of multiresolution analysis based on the theory of spectral pairs was considered by Gabardo and Nashed [4] for which the translation set Λ = {0, r/N}+2 ℤ is no longer a discrete subgroup of ℝ but a spectrum associated with a certain one-dimensional spectral pair. In this short communication, we characterize the scaling functions associated with such a nonuniform multiresolution analysis by means of some fundamental equations in the Fourier domain.

Scaling functions on the spectrum

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Scaling functions on the spectrum"}

A generalization of Mallat’s classic theory of multiresolution analysis based on the theory of spectral pairs was considered by Gabardo and Nashed [4] for...

Scaling functions on the spectrum

Published Online: Mar 04, 2019

Page range: 340 - 346

Received: May 02, 2018

DOI: https://doi.org/10.2478/ausm-2018-0026

Keywords
nonuniform multiresolution analysis, scaling function, spectrum, Fourier transform

© 2018 Abdullah et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Scaling functions on the spectrum

Published Online: Mar 04, 2019

Page range: 340 - 346

Received: May 02, 2018

DOI: https://doi.org/10.2478/ausm-2018-0026

Keywordsnonuniform multiresolution analysis, scaling function, spectrum, Fourier transform

© 2018 Abdullah et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
nonuniform multiresolution analysis, scaling function, spectrum, Fourier transform