m-Reduction of ordinary differential equations

Krystyna Skórnik; Joseph Wloka

Colloquium Mathematicae (1998)

  • Volume: 78, Issue: 2, page 195-212
  • ISSN: 0010-1354

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Skórnik, Krystyna, and Wloka, Joseph. "m-Reduction of ordinary differential equations." Colloquium Mathematicae 78.2 (1998): 195-212. <http://eudml.org/doc/210610>.

@article{Skórnik1998,
author = {Skórnik, Krystyna, Wloka, Joseph},
journal = {Colloquium Mathematicae},
keywords = {Picard-Vessiot extension; differential field; linear homogeneous differential equation; -reducibility; Galois group},
language = {eng},
number = {2},
pages = {195-212},
title = {m-Reduction of ordinary differential equations},
url = {http://eudml.org/doc/210610},
volume = {78},
year = {1998},
}

TY - JOUR
AU - Skórnik, Krystyna
AU - Wloka, Joseph
TI - m-Reduction of ordinary differential equations
JO - Colloquium Mathematicae
PY - 1998
VL - 78
IS - 2
SP - 195
EP - 212
LA - eng
KW - Picard-Vessiot extension; differential field; linear homogeneous differential equation; -reducibility; Galois group
UR - http://eudml.org/doc/210610
ER -

References

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  1. C. Chevalley, Séminaire sur la classification de groupes de Lie algébriques, École Norm. Sup., Paris, 1956-1958. 
  2. J. E. Humphreys, Linear Algebraic Groups, Springer, Berlin, 1975. Zbl0325.20039
  3. E. L. Ince, Ordinary Differential Equations, Dover, New York, 1956. Zbl0063.02971
  4. I. Kaplansky, An Introduction to Differential Algebra, Hermann, Paris, 1976. Zbl0083.03301
  5. E. R. Kolchin, Algebraic matrix groups and Picard-Vessiot theory of homogeneous linear ordinary differential equations, Ann. of Math. 49 (1948), 1-42. Zbl0037.18701
  6. E. R. Kolchin, Differential Algebra and Algebraic Groups, Academic Press, New York, 1973. Zbl0264.12102
  7. S. Lang, Algebra, Addison-Wesley, Reading, 1984. 
  8. A. R. Magid, Lectures on Differential Galois Theory, Amer. Math. Soc., 1994. Zbl0855.12001
  9. Yu. I. Merzlyakov, Rational Groups, Nauka, Moscow, 1980 (in Russian). 
  10. J. Mikusiński, Operational Calculus, Pergamon Press, New York, 1959. Zbl0088.33002
  11. K. Skórnik and J. Wloka, Factoring and splitting of s-differential equations in the field of Mikusiński, Integral Transforms and Special Functions 4 (1996), 263-274. Zbl0862.34005
  12. M. F. Singer, Solving homogeneous linear differential equations in terms of second order linear differential equations, Amer. J. Math. 107 (1985), 663-696. Zbl0564.12022
  13. M. F. Singer, Algebraic relations among solutions of linear differential equations: Fano's theorem, ibid. 110 (1988) 115-144. Zbl0651.12016
  14. M. F. Singer, An outline of differential Galois theory, in: Computer Algebra and Differential Equations, E. Tournier (ed.), Academic Press, London, 1989, 3-57. 
  15. C. Tretkoff and M. Tretkoff, Solution of the inverse problem of differential Galois theory in the classical case, Amer. J. Math. 101 (1979), 1327-1332. Zbl0423.12021
  16. J. T. Wloka, Über lineare s-Differentialgleichungen in der Operatorenrechnung, Math. Ann. 166 (1966), 233-256. Zbl0148.36901
  17. A. E. Zalesskij, Linear groups, in: Algebra IV, Encyclopaedia Math. Sci. 37, Springer, Berlin, 1993, 97-196. 

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