ArticleOriginal scientific text

Title

m-Reduction of ordinary differential equations

Authors 1, 2

Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Staromiejska 8/6, 40-013 Katowice, Poland
  2. Mathematisches Seminar der Universität Kiel, Ludewig-Meyn-Str. 4, D-24098 Kiel, Germany

Bibliography

  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.
  3. E. L. Ince, Ordinary Differential Equations, Dover, New York, 1956.
  4. I. Kaplansky, An Introduction to Differential Algebra, Hermann, Paris, 1976.
  5. E. R. Kolchin, Algebraic matrix groups and Picard-Vessiot theory of homogeneous linear ordinary differential equations, Ann. of Math. 49 (1948), 1-42.
  6. E. R. Kolchin, Differential Algebra and Algebraic Groups, Academic Press, New York, 1973.
  7. S. Lang, Algebra, Addison-Wesley, Reading, 1984.
  8. A. R. Magid, Lectures on Differential Galois Theory, Amer. Math. Soc., 1994.
  9. Yu. I. Merzlyakov, Rational Groups, Nauka, Moscow, 1980 (in Russian).
  10. J. Mikusiński, Operational Calculus, Pergamon Press, New York, 1959.
  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.
  12. M. F. Singer, Solving homogeneous linear differential equations in terms of second order linear differential equations, Amer. J. Math. 107 (1985), 663-696.
  13. M. F. Singer, Algebraic relations among solutions of linear differential equations: Fano's theorem, ibid. 110 (1988) 115-144.
  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.
  16. J. T. Wloka, Über lineare s-Differentialgleichungen in der Operatorenrechnung, Math. Ann. 166 (1966), 233-256.
  17. A. E. Zalesskij, Linear groups, in: Algebra IV, Encyclopaedia Math. Sci. 37, Springer, Berlin, 1993, 97-196.
Pages:
195-212
Main language of publication
English
Received
1997-03-05
Accepted
1998-03-15
Published
1998
Exact and natural sciences