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Zbl 0651.34039
Votava, Milan
Einige Eigenschaften der verallgemeinerten Polarfunktion und der Radonschen Funktion. (Some properties of the generalized polar functions and of the Radon function). (German)
[J] Acta Univ. Palacki. Olomuc., Fac. Rerum Nat. 85, Math. 25, 117-131 (1986). ISSN 0231-9721

{\it O. Boruuvka} [Linear differential transformations of the second order (1971; Zbl 0222.34002)] introduced the concept of phase functions for a basis $(u,v)$ of solutions of a differential equation $y''+q(t)y=0$. The first and second phases $\alpha(t)$ and $\beta(t)$ are defined by $\tan\alpha=u/v$ and tan $\beta$ $=u'/v'$. A polar function is defined by $\theta =\beta -\alpha$, and a Radon function by $\zeta =\beta +\alpha$. Boruuvka, [loc. cit.] gives several formulas and applications for these concepts. The present paper is a contribution to the study of these formulas in the more general situation where, for the second phase, we consider $(\omega u+u',\omega v+v')$ rather than $(u',v')$, where $\omega(t)$ is a suitable function.
[M.E.Muldoon]

MSC 2000:: *34C20 Transformation of ODE and systems

Keywords: phase functions; polar function; Radon function

Citations: Zbl 0222.34002

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