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.
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