2020/08/20 by Owais Ahmad, Ahmad, Owais, Neyaz A. Sheikh +3 · 1 citation
Mathematics · #Mathematical Analysis and Transform Methods #Approximation Theory and Sequence Spaces #Fractional Differential Equations Solutions
paper · pdf · doi:10.48550/arxiv.2008.09609
In this paper, we show how to construct an orthonormal basis from Riesz basis\nby assuming that the fractional translates of a single function in the core\nsubspace of the fractional multiresolution analysis form a Riesz basis instead\nof an orthonormal basis. In the definition of fractional multiresolution\nanalysis, we show that the intersection triviality condition follows from the\nother conditions. Furthermore, we show that the union density condition also\nfollows under the assumption that the fractional Fourier transform of the\nscaling function is continuous at 0. At the culmination, we provide the\ncomplete characterization of the scaling functions associated with fractional\nmultiresolutrion analysis.\n