Rational approximations to fractional powers of self-adjoint positive operators

We investigate the rational approximation of fractional powers of unbounded positive operators attainable with a specific integral representation of the operator function. We provide accurate error bounds by exploiting classical results in approximation theory involving Padé approximants. The analysis improves some existing results and the numerical experiments proves its accuracy. "The research that led to the present paper was partially supported by a grant of the group GNCS of INdAM "