English

Fractional calculus for power functions

Analysis of PDEs 2011-10-27 v2 Probability

Abstract

We calculate the fractional Laplacian for functions of the form u(x)=(1x2)+pu(x)=(1-|x|^2)_+^p and v(x)=xdu(x)v(x)=x_d u(x). As an application, we estimate the first eigenvalues of the fractional Laplacian in a ball.

Keywords

Cite

@article{arxiv.1103.3387,
  title  = {Fractional calculus for power functions},
  author = {Bartłomiej Dyda},
  journal= {arXiv preprint arXiv:1103.3387},
  year   = {2011}
}

Comments

18 pages, added Proposition 2 and references, some minor corrections

R2 v1 2026-06-21T17:40:48.106Z