ABSTRACT
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 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.
Acknowledgements
On the Belarusian side, the work was carried out within the framework of the Special Project of Fundamental and Applied Scientific Research of the National Academy of Sciences of Belarus “Investigation of the properties of spectra of discrete systems under perturbations of their coefficients.”
Disclosure statement
No potential conflict of interest was reported by the authors.