Representation of multipliers on spaces of real analytic functions (Q2872888)

The paper deals with multipliers on spaces of real analytic functions and their representations. The paper is divided into six parts. In the introductory section, the authors explain their motivation for their research as well as some background. The most fundamental results are contained in Section 2 -- representations of multipliers in terms of analytic functionals and, consequently, of holomorphic functions. The next section is devoted to dilation sets. Section 4 describes Euler differential operators acting on spaces of real analytic functions of one variable. This is then followed by the characterization of these operators among multipliers. Section 5 is a more detailed treatment of spaces of analytic functions defined on an open set \(I\subset\mathbb{R}\) not containing zero. Here the third representation theorem comes. The main application of the above results appears in the final section, where the authors characterize surjective multipliers and surjective Euler differential operators.