Some Special Two-dimensional Series of $\{\sin x\sin kx\}$ System and Their Approximation Properties

In present paper there were introduced two-dimensional special series of the system $\{\sin x\sin kx\}$. It's shown that these series have the advantage over two-dimensional cosine Fourier series, because they have better approximation properties near the bounds of the square $[0,1]^2$. It's given convergence speed estimate of special series partial sums to functions $f(x,y)$ from the space of even $2\pi$-periodic continuous functions.