Real analytic zero solutions of linear partial differential operators with constant coefficients

It is shown that for a wide class of linear partial differential operators with constant coefficients the space of real analytic zero solutions does not admit a Schauder basis. This is based on results on the linear topological structure of the space of zero solutions and a careful analysis of the s...

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Bibliographic Details
Published in:Bulletin of the Belgian Mathematical Society, Simon Stevin Simon Stevin, 2007, Vol.14 (3), p.577-586
Main Author: Vogt, Dietmar
Format: Article
Language:English
Subjects:
26E05
35E20
46E10
linear partial differential operators
real analytic functions
Schauder basis
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Summary:It is shown that for a wide class of linear partial differential operators with constant coefficients the space of real analytic zero solutions does not admit a Schauder basis. This is based on results on the linear topological structure of the space of zero solutions and a careful analysis of the solvability with a real analytic parameter.
ISSN:1370-1444
2034-1970
DOI:10.36045/bbms/1190994220