On two-dimensional linear spaces of continuous functions of the same character. (English) Zbl 0704.34044

Summary: This paper presents a necessary and sufficient condition for the existence of a global transformation of a strongly regular space of continuous functions onto a strongly regular space of continuous functions. The results obtained are then applied to spaces of solutions of second order linear differential equations of a general form \(y''+a(t)y'+b(t)y=0,\) where \(a,b\in C^{(0)}(j)\) and of the Sturm form \((p(t)y')'+q(t)y=0,\) where \(p,q\in C^{(0)}(j)\), \(py'\in C^{(1)}(j)\), p(t)\(\neq 0\) in j, whereby \(C^{(0)}(j)\) and \((C^{(1)}(j))\) respectively denote the set of all continuous functions and the set of all functions with a continuous first derivative, on the interval j.


34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
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