PROPERTIES OF THE SPECTRUM FOR THE SINGULAR DIFFUSION OPERATOR
ABDULLAH ERGÜN *
Vocational School of Sivas, Cumhuriyet University, 58140 Sivas, Turkey.
Department of Mathematics, Faculty of Science and Arts, Cumhuriyet University, 58140 Sivas, Turkey.
*Author to whom correspondence should be addressed.
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.
Keywords: Integral equation, Sturm-Liouville operator, diffusion operator, spectral problem.