On 1-regular ordinary differential operators

ArticleOriginal scientific text

Title

Authors ¹

Institute of Mathematics, Polish Academy of Sciences, P.O. Box 137, Śniadeckich 8, 00-950 Warszawa, Poland

Solutions to singular linear ordinary differential equations with analytic coefficients are found in the form of Laplace type integrals.

singular differential equations, Mellin transformation, Laplace integrals

[B] B. L. J. Braaksma, Multisummability and Stokes multipliers of linear meromorphic differential equations, J. Differential Equations 92 (1991), 45-75.
[CL] A. E. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.
[E] J. Ecalle, Introduction à l'accélération et à ses applications, Travaux en Cours, Hermann, 1993.
[K] H. Komatsu, Ultradistributions, I. Structure theorems and a characterization, J. Fac. Sci. Univ. Tokyo 20 (1973), 25-105.
[Ł1] G. Łysik, On extendible ultradistributions, Bull. Polish Acad. Sci. Math. 43 (1995), 29-40.
[Ł2] G. Łysik, Laplace ultradistributions on a half line and a strong quasi-analyticity principle, Ann. Polon. Math. 63 (1996), 13-33.
[Ł3] G. Łysik, The Mellin transformation of strongly increasing functions, J. Math. Sci. Univ. Tokyo 6 (1999), 49-86.
[M] B. Malgrange, Sommation des séries divergentes, Exposition. Math. 13 (1995), 163-222.
[T] J. C. Tougeron, Gevrey expansions and applications, preprint, Univ. of Toronto, 1991.
[Z] B. Ziemian, Generalized analytic functions with applications to singular ordinary and partial differential equations, Dissertationes Math. 354 (1996).