Exact errors of best approximation for complex-valued nonperiodic functions

We extend Markov's and Nagy's theorems on best approximation by entire functions of exponential type in the L1(R) metric to some complex-valued integrable and locally integrable functions. We use these results for finding sharp constants of best approximation in L1(R) and L∞(R) on some complex convolution classes. For classes of real-valued convolutions those constants were found by Akhiezer. As an example, we apply these results to the Schwarz-type kernel and to the corresponding convolution classes.