The Evolution Function of the Operator − (−Δ)v

Resumo

The evolution function of the differential operator −(−Δ)^v in a d-dimensional Euclidean space is calculated. We obtain its analytic expression through the Fox-Wright psi-functions, which is well-defined for both integer and noninteger values of v and d. Possible applications of the obtained functions in quantum field theory and the connection with fractional calculus are discussed.