Fractional calculus for power functions

preprint2011arXivOpen access

We calculate the fractional Laplacian for functions of the form $u(x)=(1-|x|^2)_+^p$ and $v(x)=x_d u(x)$ . As an application, we estimate the first eigenvalues of the fractional Laplacian in a ball.

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Fractional calculus for power functions

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