  The paper studies Sard's problem on construction of optimal quadrature
formulas in the space $W_2^{(m,0)}$ by Sobolev's method. This problem consists
of two parts: first calculating the norm of the error functional and then
finding the minimum of this norm by coefficients of quadrature formulas. Here
the norm of the error functional is calculated with the help of the extremal
function. Then using the method of Lagrange multipliers the system of linear
equations for coefficients of the optimal quadrature formulas in the space
$W_2^{(m,0)}$ is obtained, moreover the existence and uniqueness of the
solution of this system are discussed. Next, the discrete analogue
$D_m(h\beta)$ of the differential operator $\frac{d^{2m}}{d x^{2m}}-1$ is
constructed. Further, Sobolev's method of construction of optimal quadrature
formulas in the space $W_2^{(m,0)}$, which based on the discrete analogue
$D_m(h\beta)$, is described. Finally, for $m=1$ and $m=3$ the optimal
quadrature formulas which are exact to exponential-trigonometric functions are
obtained.
