Multiplier projections on spaces of real analytic functions in several variables.

Letbe open with. We characterize the setshaving the following property: for every real analytic functionfonwith Taylor expansionat zero, the seriesis also the Taylor expansion at zero of some real analytic function on. This result gives a characterization of the idempotents in the algebraof 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 onand the (continuous) algebra homomorphisms. We show that the algebrais never locally m-convex and in many cases it is not a Q-algebra. [ABSTRACT FROM AUTHOR]