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A description of the spectrum of Sergeev frequencies of zeros of linear difference equations. (English) Zbl 1505.39001

Summary: We prove that the spectra (sets of values) of the upper and lower Sergeev frequencies of zeros of a linear difference equation of order higher than one are Suslin sets of the interval \([0,1]\). Moreover, we prove the inverse theorem for upper frequencies of zeros of second-order equations under the additional assumption that 0 belongs to the spectrum.

MSC:

39A06 Linear difference equations
39A21 Oscillation theory for difference equations
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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