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- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature 2021
- ISSN
- 1664-2368
- eISSN
- 1664-235X
- DOI
- 10.1007/s13324-021-00481-9
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, we show how to construct an orthonormal basis from Riesz basis by assuming that the fractional translates of a single function in the core subspace of the fractional multiresolution analysis form a Riesz basis instead of an orthonormal basis. In the definition of fractional multiresolution analysis, we show that the intersection triviality condition follows from the other conditions. Furthermore, we show that the union density condition also follows under the assumption that the fractional Fourier transform of the scaling function is continuous at 0. At the culmination, we provide the complete characterization of the scaling functions associated with fractional multiresolution analysis.
Journal
Analysis and Mathematical Physics – Springer Journals
Published: Feb 6, 2021