Bulletin of the Belgian Mathematical Society - Simon Stevin

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

Dietmar Vogt

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Abstract

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.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 14, Number 3 (2007), 577-586.

Dates
First available in Project Euclid: 28 September 2007

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1190994220

Digital Object Identifier
doi:10.36045/bbms/1190994220

Mathematical Reviews number (MathSciNet)
MR2387056

Zentralblatt MATH identifier
1133.46015

Subjects
Primary: 46E10: Topological linear spaces of continuous, differentiable or analytic functions
Secondary: 26E05: Real-analytic functions [See also 32B05, 32C05] 35E20: General theory

Keywords
real analytic functions linear partial differential operators Schauder basis

Citation

Vogt, Dietmar. Real analytic zero solutions of linear partial differential operators with constant coefficients. Bull. Belg. Math. Soc. Simon Stevin 14 (2007), no. 3, 577--586. doi:10.36045/bbms/1190994220. https://projecteuclid.org/euclid.bbms/1190994220


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