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Representation of multipliers on spaces of real analytic functions

✍ Scribed by Domański, Paweł; Langenbruch, Michael

Book ID
120633393
Publisher
Oldenbourg Wissenschaftsverlag
Year
2012
Tongue
English
Weight
211 KB
Volume
32
Category
Article
ISSN
0174-4747

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✦ Synopsis

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. Then we characterize when such operators are surjective or have a continuous linear right inverse on the space of real analytic functions over an interval not containing zero. In particular we solve the problem when Euler differential equation of infinite order has a solution in the space of real analytic functions on an interval not containing zero.

📜 SIMILAR VOLUMES

Composition operators on spaces of real
Composition operators on spaces of real analytic functions
✍ Paweł Domański; Michael Langenbruch 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 259 KB 👁 1 views

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