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Symmetric Decomposition of f ∈ L2(R) Via Fractional Riemann-Liouville Operators |
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PP: 143-151 |
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doi:10.18576/pfda/060207
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Author(s) |
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Yulong Li,
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Abstract |
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| 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.
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