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Explicit invariant solutions for invariant linear differential operators

Published online by Cambridge University Press:  14 November 2011

Zofia Szmydt  and
Bogdan Ziemian
Zofia Szmydt
Affiliation:
Instytut Matematyczny, Polska Akademia Nauk, Ul Sniadeckich 8, Warszawa, Poland
Bogdan Ziemian
Affiliation:
Instytut Matematyczny, Polska Akademia Nauk, Ul Sniadeckich 8, Warszawa, Poland
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Synopsis

Let F be a real analytic function on a real analytic manifold X. Let P be a linear differential operator on X such that , where Q is an ordinary differential operator with analytic coefficients whose singular points are all regular. For each (isolated) critical value z of F, we construct locally an F-invariant solution u of the equation Pu - v, v being an arbitrary F-invariant distribution supported in F−1(z). The solution u is constructed explicitly in the form of a series of F-invariant distributions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 98 , Issue 1-2 , 1984 , pp. 149 - 166
Copyright
Copyright © Royal Society of Edinburgh 1984

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