## To the theory of central dispersions for the linear differential equations $$y''=q(t)y$$ of a finite type-special.(English)Zbl 0708.34011

The author presents a certain generalization of the basic concepts involved in Borůvka’s theory of central dispersions for the differential equation $$y''=q(t)y$$ on an interval (a,b) with $$-\infty \leq a<b\leq +\infty$$. She introduces special central dispersions $$\phi_ n(t)$$ and $$\psi_ n(t)$$ of first and second kind with arbitrary index n and studies certain algebraic properties of the sets $$G^{(1)}$$ and $$G^{(2)}$$ which these functions constitute. Introducing still another two kinds of dispersions she obtains finally the set $$\Gamma =G^{(1)}\cup G^{(2)}\cup G^{(3)}\cup G^{(4)}$$ of special central dispersions and shows that $$\Gamma$$ consists of two finite cyclic groups and two finite sets.
Reviewer: L.Janos

### MSC:

 34A30 Linear ordinary differential equations and systems
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### References:

 [1] Borůvka O.: Lineare Differentialtransformationen 2.Ordnung. VEB OVW, Berlin 1967. · Zbl 0153.11201 [2] Laitoch M.: To the theory of linear difference equations. Acta Univ. Palackianae Olomucensis (Olomouc), Fac. Rer. Nat. 79 (1984). · Zbl 0586.39002
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