Derivatives on Function Spaces Generated By the Dirichlet Laplacian and the Neumann Laplacian in One Dimension

Abstract

We investigate the relation between Besov spaces generated by the Dirichlet Laplacian and the Neumann Laplacian in one space dimension from the view point of the boundary value of functions. Derivatives on spaces with such boundary conditions are defined, and it is proved that the derivative operator is isomorphic from one to the other.