3
votes
3answers
1k views

Fourier transform of fractional differential operator and Plancherel formula equivalent for fractional norms

I would like to know if the the following exist or are defined The Fourier transform $\mathcal{F}\left(\frac{d^{\frac{1}{2}}y}{dx^\frac{1}{2}}\right)$ of a fractional differential operator such as ...