Fractional $\frac{1}{2}$-Laplacian of holomorphic functions via Jacobi polynomials

Fabrizio Colombo, Antonino De Martino, Alberto Debernardi Pinos

We give a distributional definition of the $\frac{1}{2}$-fractional Laplacian for smooth functions with power-type singularities at the origin, including negative monomials and cer…