• Corpus ID: 119755129

Symmetric Decompositions of $f\in L^2(\mathbb{R})$ Via Fractional Riemann-Liouville Operators

@article{Li2018SymmetricDO,
title={Symmetric Decompositions of \$f\in L^2(\mathbb\{R\})\$ Via Fractional Riemann-Liouville Operators},
author={Yulong Li},
journal={arXiv: Classical Analysis and ODEs},
year={2018}
}
• Yulong Li
• Published 5 July 2018
• Mathematics
• arXiv: Classical Analysis and ODEs
It is proved that given $-1/2<s<1/2$, for any $f\in L^2(\mathbb{R})$, there is a unique $u\in \widehat{H}^{|s|}(\mathbb{R})$ such that $$f=\boldsymbol{D}^{-s}u+\boldsymbol{D}^{s*}u\,,$$ where $\boldsymbol{D}^{-s}, \boldsymbol{D}^{s*}$ are fractional Riemann-Liouville operators and the fractional derivatives are understood in the weak sense. Furthermore, the regularity of $u$ is discussed, and other versions of the results are established. As an interesting consequence, the Fourier transform…

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