PROPERTIES OF THE SPECTRUM FOR THE SINGULAR DIFFUSION OPERATOR

In this study, singular diffusion operator is considered, we have derived integral equations for the solutions under certain initial conditions. We have also derived integral representations that satisfy initial conditions. Some features of the zeros of the characteristic functions have been obtained and with the help of these, we have investigated spectral properties of singular diffusion operator. Furthermore, we have obtained the asymptotic formulas for eigenvalues, eigenfunctions and normalizing numbers.