Scaling functions on the spectrum

Abdullah; Firdous A. Shah

doi:10.2478/ausm-2018-0026

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Scaling functions on the spectrum

Acta Universitatis Sapientiae, Mathematica

Volume 10 (2018): Issue 2 (December 2018)

By: Abdullah and Firdous A. Shah

Open Access

|Mar 2019

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.

References

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Articles in this issue

DOI: https://doi.org/10.2478/ausm-2018-0026 | Journal eISSN: 2066-7752

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Language: English

Page range: 340 - 346

Submitted on: May 2, 2018

Published online: Mar 4, 2019

Published in print: Dec 1, 2018

Published by: Sapientia Hungarian University of Transylvania

In partnership with: Paradigm Publishing Services

Keywords:

nonuniform multiresolution analysis,

scaling function,

spectrum,

Fourier transform

MSC:

42C15,

42C40,

65T60

Related subjects:

Mathematics,

General mathematics

© 2019 Abdullah, Firdous A. Shah, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 10 (2018): Issue 2 (December 2018)