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Die Kummerschen Transformationen in Räumen mit abgeschlossenen Phasen. A: Allgemeine Eigenschaften. (German) Zbl 0216.10902
The paper is a direct continuation of the author’s previous work [Spisy Prirod. Fak. Univ. J. E. Purkyne Brne 1966, 389–410 (1966; Zbl 0256.34007); Arch. Math., Brno 3, 117–138 (1967; Zbl 0217.40002)] on the transformations of two-dimensional spaces of functions defined on an interval. The main result of the present paper states that the transformation invariants of any such space can be formulated in terms of the functions that vanish at the endpoints of the interval and that such functions exist in any real two-dimensional space. The main tool is that of the phase, the polar angle of the curve described by an arbitrary element of the space.
For Part B: “Transformationen in Räumen der gegebenen Klasse” see Zbl 0244.34005.
Reviewer: H. W. Guggenheimer
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34A30 Linear ordinary differential equations and systems
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