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Hadamard multipliers on spaces of real analytic functions

✍ Scribed by Domański, Paweł; Langenbruch, Michael

Book ID
120260684
Publisher
Elsevier Science
Year
2013
Tongue
English
Weight
497 KB
Volume
240
Category
Article
ISSN
0001-8708

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We consider multipliers on the spaces of real analytic functions of one variable, i.e., maps for which monomials are eigenvectors. We prove representation theorems in terms of analytic functionals and in terms of holomorphic functions. We characterize Euler differential operators among multipliers.

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Let Ω1, Ω2 be open subsets of R d 1 and R d 2 , respectively, and let A(Ω1) denote the space of real analytic functions on Ω1. We prove a Glaeser type theorem by characterizing when a composition operator Cϕ : Using this result we characterize when A(Ω1) can be embedded topologically into A(Ω2) as