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Fractional calculus for power functions

Published 17 Mar 2011 in math.AP and math.PR | (1103.3387v2)

Abstract: 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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Authors (1)

  1. Bartłomiej Dyda 

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