Abstract:
We consider the problem
of mean-square approximation of analytic functions in simply
connected domain of complex plane with Fourier series by orthogonal
in the domain of system of functions. For the some class of analytic
functions in unit disk the supremum of mean-square approximation
given by special module of continuity were calculated.
Keywords:supremum, module of continuity, Jackson–Stechkin inequality, $n$-widths, $\mathscr{K}$-functional.
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