Multiplier projections on spaces of real analytic functions in several variables

Abstract

Let be open with . We characterize the sets having the following property: for every real analytic function f on with Taylor expansion at zero, the series is also the Taylor expansion at zero of some real analytic function on . This result gives a characterization of the idempotents in the algebra of Hadamard-type operators on the space of all real analytic functions , i.e. operators with all monomials being eigenvectors. In many cases, we also describe the multiplicative functionals on and the (continuous) algebra homomorphisms . We show that the algebra is never locally m-convex and in many cases it is not a Q-algebra.