Multiplier projections on spaces of real analytic functions in several variables

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 o...

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Bibliographic Details
Published in:Complex variables and elliptic equations Vol. 62; no. 2; pp. 241 - 268
Main Authors: Domański, Paweł, Langenbruch, Michael
Format: Journal Article
Language:English
Published: Colchester Taylor & Francis 01.02.2017
Taylor & Francis Ltd
Subjects:
Algebra
algebra homomorphisms
Analytic functions
Complex variables
Hadamard-type multiplier
Homomorphisms
invertible elements
locally m-convex algebra
Mathematical analysis
multiplicative functionals
Operators (mathematics)
power series with finitely many values of coefficients
Primary: 32D15
Projection
Q-algebra
Secondary: 32A10
Spaces of real analytic functions
Szegö theorem
topological algebra
ISSN:1747-6933, 1747-6941
Online Access:Get full text
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Summary: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.
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ISSN:1747-6933
1747-6941
DOI:10.1080/17476933.2016.1218854