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To the theory of linear difference equations with constant coefficients. (English) Zbl 0695.39001

The functional equation generalizing the classical difference equation, namely the equation \((1)\quad c_ kf[\phi_{n+k}(t)]+...+c_ 0f[\phi_ n(t)]=g[\phi_ n(t)]\) with certain initial conditions is considered.
In equation (1) the coefficients \(c_ 0,...,c_ k\) are real constant numbers and \(c_ k\neq 0\), the function g is real function defined in the interval (-\(\infty,\infty)\) and the functions \(\phi_ i(t)\) are elements of the group of the first kind central dispersions of the oscillatory differential equation \(y''=q(t)y.\)
The author proves that the solution f(t) of equation (1) is determined uniquely. Moreover, the author using an operational method gives the solution f(t) in closed form.
Reviewer: S.Kus

MSC:

39A10 Additive difference equations
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References:

[1] Feldmann L.: On linear difference equations with constant coefficients. Periodica Polytechnica El. III/3, Budapest, 25.11.1958.
[2] Fenyö I.: Eine neue Methode zur Lösung von Differenzengleichungen nebst Anwendungen. Elektrotechnische Fakultät der Technischen Universität, Budapest, 10.12.1958.
[3] Zypkin J. S.: Differenzengleichungen der Impuls- und Regeltechnik. 1956, Berlin. · Zbl 0070.33203
[4] Borůvka O.: Lineare Differentialtransformationen 2.0rdnung. VEB DVW 1967, Berlin.
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