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To the definition of the global transformation in 2-dimensional linear spaces of continuous functions. (English) Zbl 0715.34012

Summary: We study the question relating to the equivalence of definitions of the global transformation in two 2-dimensional linear spaces of continuous functions. We apply the definitions of transformation introduced by O. Borůvka [Lineare Differentialtransformationen 2. Ordnung. Berlin (1967; Zbl 0153.112); Englisch translation: London 1971], F. Neumann [Differ. Equations 19, 571-580 (1983); translation from Differ. Uravn. 19, No.5, 799-808 (1983; Zbl 0524.34044)] and K. Stach [Arch. Math., Brno 3, 117-138 (1967; Zbl 0217.400)], in studying the spaces of solutions of the second-order linear differential equations in the Jacobian form, the spaces of solutions of the nth order homogeneous linear differential equations, the 2-dimensional linear spaces of continuous functions, respectively.

MSC:

34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34A30 Linear ordinary differential equations and systems
34G10 Linear differential equations in abstract spaces
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References:

[1] Borůvka O.: Linear Differential Transformations of the Second Order. The English University Press, London 1971. · Zbl 0218.34005
[2] Неуман Ф.: Теория глобальных свойств обыкновенных линейных дифференциальных уравнений н-го порядка. Дифференциальные уравнения 19 (1983), 799-808. · Zbl 1229.47001
[3] Stach K.: Die vollständigen Kummerschen Transformationen zweidimensionaler Räume von stetigen Funktionen. Arch. Math. Brno, T3 (1967), 117-138. · Zbl 0217.40002
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