Define $\hat{f}(\xi)\equiv F(f)(\xi):=\int_{\mathbb{R}}e^{ix.\xi}f(x)dx $
My question is: if we consider $x^{\alpha}$ as a distribution then what is $ F(x^{\alpha})(\xi)$ where $0<\alpha\in\mathbb{R}$. thanks
Define $\hat{f}(\xi)\equiv F(f)(\xi):=\int_{\mathbb{R}}e^{ix.\xi}f(x)dx $
My question is: if we consider $x^{\alpha}$ as a distribution then what is $ F(x^{\alpha})(\xi)$ where $0<\alpha\in\mathbb{R}$. thanks