On 1-regular ordinary differential operators

Grzegorz Łysik

Annales Polonici Mathematici (2000)

  • Volume: 74, Issue: 1, page 201-214
  • ISSN: 0066-2216

Abstract

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

How to cite

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Łysik, Grzegorz. "On 1-regular ordinary differential operators." Annales Polonici Mathematici 74.1 (2000): 201-214. <http://eudml.org/doc/208366>.

@article{Łysik2000,
abstract = {Solutions to singular linear ordinary differential equations with analytic coefficients are found in the form of Laplace type integrals.},
author = {Łysik, Grzegorz},
journal = {Annales Polonici Mathematici},
keywords = {singular differential equations; Mellin transformation; Laplace integrals; 1-regular ordinary differential operators; solutions; Laplace type integrals},
language = {eng},
number = {1},
pages = {201-214},
title = {On 1-regular ordinary differential operators},
url = {http://eudml.org/doc/208366},
volume = {74},
year = {2000},
}

TY - JOUR
AU - Łysik, Grzegorz
TI - On 1-regular ordinary differential operators
JO - Annales Polonici Mathematici
PY - 2000
VL - 74
IS - 1
SP - 201
EP - 214
AB - Solutions to singular linear ordinary differential equations with analytic coefficients are found in the form of Laplace type integrals.
LA - eng
KW - singular differential equations; Mellin transformation; Laplace integrals; 1-regular ordinary differential operators; solutions; Laplace type integrals
UR - http://eudml.org/doc/208366
ER -

References

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  1. [B] B. L. J. Braaksma, Multisummability and Stokes multipliers of linear meromorphic differential equations, J. Differential Equations 92 (1991), 45-75. Zbl0729.34005
  2. [CL] A. E. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955. Zbl0064.33002
  3. [E] J. Ecalle, Introduction à l'accélération et à ses applications, Travaux en Cours, Hermann, 1993. 
  4. [K] H. Komatsu, Ultradistributions, I. Structure theorems and a characterization, J. Fac. Sci. Univ. Tokyo 20 (1973), 25-105. Zbl0258.46039
  5. [Ł1] G. Łysik, On extendible ultradistributions, Bull. Polish Acad. Sci. Math. 43 (1995), 29-40. Zbl0823.46038
  6. [Ł2] G. Łysik, Laplace ultradistributions on a half line and a strong quasi-analyticity principle, Ann. Polon. Math. 63 (1996), 13-33. Zbl0843.46025
  7. [Ł3] G. Łysik, The Mellin transformation of strongly increasing functions, J. Math. Sci. Univ. Tokyo 6 (1999), 49-86. Zbl0941.46023
  8. [M] B. Malgrange, Sommation des séries divergentes, Exposition. Math. 13 (1995), 163-222. Zbl0836.40004
  9. [T] J. C. Tougeron, Gevrey expansions and applications, preprint, Univ. of Toronto, 1991. 
  10. [Z] B. Ziemian, Generalized analytic functions with applications to singular ordinary and partial differential equations, Dissertationes Math. 354 (1996). Zbl0868.46034

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