The best $L_1$-approximations of classes of functions defined by differential operators in terms of generalized splines from these classes
Ukr. Mat. Zh. - 1998. - 50, № 11. - pp. 1443-1451
For classes of periodic functions defined by constraints imposed on the $L_1$-norm of the result of action of differential operators with constant coefficients and real spectrum on these functions, we determine the exact values of the best $L_1$-approximations by generalized splines from the classes considered.