Abstract
In this chapter, we introduce linear and non linear singular operators D acting on formal power series and we study the operators having the property of “regular singularity”. This means that we give conditions on D to have the following property:
“if û is a formal power series such that Dû converges then û is a convergent power series”.
This study gives us then very interesting applications to differential equations and gives new proofs for classical results.
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© 1996 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
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Gérard, R., Tahara, H. (1996). Operators with regular singularities: One variable case. In: Singular Nonlinear Partial Differential Equations. Aspects of Mathematics, vol 28. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-80284-2_1
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DOI: https://doi.org/10.1007/978-3-322-80284-2_1
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-322-80286-6
Online ISBN: 978-3-322-80284-2
eBook Packages: Springer Book Archive