The best L 1-approximations of classes of functions defined by differential operators in terms of generalized splines from these classes

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. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1443–1451, November, 1998.