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LINEAR CONTINUOUS EXTENSION OPERATORS FOR GEVREY CLASSES ON POLYSECTORS

Published online by Cambridge University Press:  31 July 2003

J. SANZ
J. SANZ
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Valladolid, c/Prado de la Magdalena s/n, 47005 Valladolid, Spain e-mail: jsanzg@am.uva.es
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Abstract

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We study Gevrey classes of holomorphic functions of several variables on a polysector, and their relation to classes of Gevrey strongly asymptotically developable functions. A new Borel-Ritt-Gevrey interpolation problem is formulated, and its solution is obtained by the construction of adequate linear continuous extension operators. Our results improve those given by Haraoka in this context, and extend to several variables the one-dimensional versions of the Borel-Ritt-Gevrey theorem given by Ramis and Thilliez, respectively. Some rigidity properties for the constructed operators are stated.

Keywords

30D6030E0541A60
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 45 , Issue 2 , May 2003 , pp. 199 - 216
Copyright
2003 Glasgow Mathematical Journal Trust