Fractional powers of the wave operator via Dirichlet-to-Neumann maps in   anti-de Sitter spaces
  We show that the fractional wave operator, which is usually studied in the context of hypersingular integrals but had not yet appeared in mathematical physics, can be constructed as the Dirichlet-to-Neumann map associated with the Klein-Gordon equation in anti-de Sitter spacetimes. Several generalizations of this relation will be discussed too. 
Alberto Enciso, Mar\'ia del Mar Gonz\'alez and Bruno Vergara
math.AP