Kergin interpolation in Banach spaces Original Research Article

We show that Kergin interpolation, a generalized Lagrange–Hermite polynomial interpolation, may be defined on mappings between general Banach spaces. Like its finite-dimensional counterpart, Kergin interpolation in this setting is an affine-invariant projector. We obtain an error formula which we use to approximate holomorphic mappings. As an application we give a convergence theorem applicable to, for instance, operators on Banach algebras, such as the algebra of square matrices with complex coefficients.