Abstract
We completely describe the characteristic frequencies of zeros of a sum of two harmonic oscillations with distinct frequencies and partly describe the characteristic frequencies of zeros of sums of arbitrarily many oscillations. As a corollary, we show that the set of characteristic frequencies of zeros of a linear equation can be infinite and moreover have continuum measure even in the case of an equation with constant coefficients.
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Sergeev, I.N., Determination and Properties of Characteristic Frequencies of Linear Equations, Tr. Semin. im. I.G. Petrovskogo, 2006, vol. 25, no. 4, pp. 249–294.
Goritskii, A.Yu., Characteristic Frequencies of Linear Combinations of Sines, Differ. Uravn., 2008, vol. 44, no. 6, p. 860.
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Original Russian Text © A.Yu. Goritskii, T.N. Fisenko, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 4, pp. 479–486.
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Goritskii, A.Y., Fisenko, T.N. Characteristic frequencies of zeros of a sum of two harmonic oscillations. Diff Equat 48, 486–493 (2012). https://doi.org/10.1134/S0012266112040039
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DOI: https://doi.org/10.1134/S0012266112040039