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Author Country (or Countries)

USA

Abstract

The present paper proves that given −1/2 < s < 1/2, for any f ∈ L2(R), there is a unique u ∈ H􏰓|s|(R) such that f = D−su+Ds∗u, where D−s , Ds∗ are fractional Riemann-Liouville operators and the fractional derivatives are understood in the weak sense. Furthermore, regularity of u is addressed, and other versions of the results are established. Consequently, the Fourier transform of elements of L2(R) is characterized.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/060207

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