Fractional powers of non-negative operators in Banach spaces via the Dirichlet-to-Neumann operator

Abstract

We consider fractional powers of non-densely defined non-negative operators in Banach spaces defined by means of the Balakrishnan operator. Under mild assumptions on the operator we show that the fractional powers can partially be obtained by a generalised Dirichlet-to-Neumann operator for a Bessel-type differential equation.

Cited by in corpus (2)

• On the harmonic extension approach to fractional powers in Banach spaces
• A series representation of the discrete fractional Laplace operator of arbitrary order