m-Reduction of ordinary differential equations

• Autorzy: Krystyna Skórnik , Joseph Wloka
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1998
• Tom: 78
• Numer: 2
• Strony: 195-212

Daty

wydano

1998

otrzymano

1997-03-05

poprawiono

1998-03-15

Twórcy

autor

Krystyna Skórnik

• Institute of Mathematics, Polish Academy of Sciences, Staromiejska 8/6, 40-013 Katowice, Poland

autor

Joseph Wloka

• Mathematisches Seminar der Universität Kiel, Ludewig-Meyn-Str. 4, D-24098 Kiel, Germany

Bibliografia

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• I. Kaplansky, An Introduction to Differential Algebra, Hermann, Paris, 1976.
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• E. R. Kolchin, Differential Algebra and Algebraic Groups, Academic Press, New York, 1973.
• S. Lang, Algebra, Addison-Wesley, Reading, 1984.
• A. R. Magid, Lectures on Differential Galois Theory, Amer. Math. Soc., 1994.
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• J. Mikusiński, Operational Calculus, Pergamon Press, New York, 1959.
• 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.
• M. F. Singer, Solving homogeneous linear differential equations in terms of second order linear differential equations, Amer. J. Math. 107 (1985), 663-696.
• M. F. Singer, Algebraic relations among solutions of linear differential equations: Fano's theorem, ibid. 110 (1988) 115-144.
• M. F. Singer, An outline of differential Galois theory, in: Computer Algebra and Differential Equations, E. Tournier (ed.), Academic Press, London, 1989, 3-57.
• 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.
• J. T. Wloka, Über lineare s-Differentialgleichungen in der Operatorenrechnung, Math. Ann. 166 (1966), 233-256.
• A. E. Zalesskij, Linear groups, in: Algebra IV, Encyclopaedia Math. Sci. 37, Springer, Berlin, 1993, 97-196.