Kojecká, Jitka Accompanying spaces to a linear two-dimensional space of continuous functions with a continuous first derivative. (English) Zbl 0534.34037 Acta Univ. Palacki. Olomuc., Fac. Rerum Nat. 73, Math. 21, 43-61 (1982). This paper investigates the properties of a linear two-dimensional space of continuous functions belonging to \(S\subset C_ 1(i)\), \(i\subset E_ 1\), with the basis \((\rho(\alpha u+\beta u)\), \(\rho(\alpha v+\beta v'))\); (u,v) is the basis of a linear two-dimensional space of continuous functions with a continuous first derivative, \(\rho>0\) is a continuous function and \(\alpha\),\(\beta (\alpha^ 2+\beta^ 2\neq 0)\) are real constants. Zeros of functions and extremes of phases relating the space \(P_{\rho}[\alpha,\beta]\) to the space S are investigated, and conditions under which this space is of the 0th class (it has no extreme points) are treated. Three basic theorems are developed. The paper is original and clearly written. Reviewer: D.E.Panayotounakos Cited in 2 Documents MSC: 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34A30 Linear ordinary differential equations and systems Keywords:Zeros of functions; extremes of phases PDF BibTeX XML Cite \textit{J. Kojecká}, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 21, 43--61 (1982; Zbl 0534.34037) Full Text: EuDML OpenURL References: [1] O. Borůvka: Lineare Differentialtransformationen 2. Ordnung. VEB Deutscher Verlag der Wissenschaften. Berlin 1967. · Zbl 0153.11201 [2] M. Laitoch: Ľéquation associée dans la théorie des transformations des équations différentielles du second ordre. Acta Univ. Palackianae 12 (1963) Olomouc. [3] K. Stach: Die allgemeinen Eigenschaften der Kummerschen Transformationen zweidimensionaler Räume von stetigen Funktionen. Publ. Fac. Sci. UJEP Brno, 478, 1966. · Zbl 0256.34007 [4] K. Stach: Die vollständigen Kummerschen Transformationen zweidimensionaler Räume von stetigen Funktionen. Archivum Math. UJEP Brno, 1967, T. 3, F. 3. · Zbl 0217.40002 [5] S. Trávníček J. Kojecká-Hodinářová: Einige Bemerkungen über die Nullstellen im zweidimensionalen Raum stetiger Funktionen. Acta Univ. Palackianae 33 (1972) Olomouc [6] J. Kojecká: Lineare zweidimensionale Räume von stetigen Funktionen mit stetigen ersten Ableitungen. Acta Univ. Palackianae 45 (1974) Olomouc. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.