SPECTRA OF THE UPPER SERGEEV FREQUENCIES OF ZEROS AND SIGNS OF LINEAR DIFFERENTIAL EQUATIONS

Abstract

It is proved that the spectra of the upper characteristic frequency of zeros and the frequency of signs (also called as the upper Sergeev frequencies) of the linear differential equations are the Suslin sets of the nonnegative semi-axis of the extended number straight line. The inverse claim is obtained under the assumption that the spectra contain zero. It is also proved that the upper Sergeev frequency of zeros and the frequency of signs, considered as the functions of initial values, are the functions of the third and second Baire classes, respectively.