Central projections of a pair of accompanying spaces to a linear two- dimensional space of functions with a continuous first derivative. (English) Zbl 0599.34044

Kojecká, Jitka

Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 22, 61-79 (1983).

M. Laitoch defined a central projection of bundles of integrals relative to the differential equation (q): \(y''=q(t)y\) with a given basis. There is considered a mapping among linear combinations \(\alpha y+\beta y'\) and \(\gamma y+\delta y'\) of the integral y relative to (q) and its derivative y’, where the numbers of bases [\(\alpha\),\(\beta\) ] and [\(\gamma\),\(\delta\) ] satisfy the condition \(\alpha\) \(\delta\)-\(\beta\) \(\gamma\) \(\neq 0\). The present paper deals with properties of a central projection of functions of a pair of accompanying spaces \(P\rho\) [\(\alpha\),\(\beta\) ] and \(P\sigma\) [\(\gamma\),\(\delta\) ] to a linear two-dimensional space of functions with a continuous first derivative.

MSC:

34C20

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

Keywords:

second order differential equation; central projection of bundles of integrals

References:

[1]	Borůvka O.: Lineare Differentialtransformationen 2. Ordnung. VEB Deutscher Verlag der Wissenschaften, Berlin 1967. · Zbl 0153.11201
[2]	Laitoch M.: Ľéquation associée dans la théorie des transformations des équations différentielles du second ordre. ACTA UP Olomouc, T. 12 (1963).
[3]	Laitoch M.: Centrální projekce svazků o dané bázi integrálů diferenciální rovnice y” = q(t)y. Rukopis - nepublikováno.
[4]	Stach K.: Die allgemeinen Eigenschaften der Kummerschen Transformationen zweidimensionaler Räume von stetigen Funktionen. Publ. Fac. Sci. UJEP Brno, 478, 1966. · Zbl 0256.34007
[5]	Stach L.: Die vollständigen Kummerschen Transformationen zweidimensionaler Räume von stetigen Funktionen. Archivum Math. UJEP Brno, 1967, T. 3, F. 3. · Zbl 0217.40002
[6]	Trávníček S., Kojecká-Hodinářová J.: Einige Bemerkungen über die Nullstellen im zweidimensionalen Raum stetiger Funktionen. ACTA UP Olomouc, T. 33 (1972).
[7]	Kojecká J.: Lineare zweidimensionale Räume von stetigen Funktionen mit stetigen ersten Ableitungen. ACTA UP Olomouc, T. 45 (1974).
[8]	Kojecká J.: Accompanying spaces to a linear two-dimensional space of continuous functions with a continuous first derivative. ACTA UP Olomouc, T. 73 (1982). · Zbl 0534.34037
[9]	Kojecká J.: On phases of accompanying spaces to a linear two-dimensional space of functions with a continuous first derivative. ACTA UP Olomouc, T. 76 (1983). · Zbl 0551.34003