On the Leading Term of the Spectral Asymptoticsfor the Zaremba–Steklov Operator in a Bounded Domain

We obtain a Weyl asymptotic formula for the number of eigenvalues of the Zaremba–Steklov operator. The leading term of the asymptotic expression is written out. The construction is based on an estimate of the Green’s function for the Dirichlet problem of the corresponding parabolic operator, and then the classical Hardy–Littlewood Tauberian theorem is applied.