On sharp estimates of the convergence of double Fourier–Bessel series

The problem of approximation of a differentiable function of two variables by partial sums of a double Fourier–Bessel series is considered. Sharp estimates of the rate of convergence of the double Fourier–Bessel series on the class of differentiable functions of two variables characterized by a generalized modulus of continuity are obtained. The proofs of four theorems on this issue, which can be directly applied to solving particular problems of mathematical physics, approximation theory, etc., are presented.