Geodesic
On the best approximation in the mean of functions of a complex variable by Fourier series in the Bergman space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2020), pp. 74-92

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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. 
@article{IVM_2020_2_a6,
     author = {M. Sh. Shabozov and Kh. M. Khuromonov},
     title = {On the best approximation in the mean of functions of a complex variable by {Fourier} series in the {Bergman} space},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {74--92},
     publisher = {mathdoc},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_2_a6/}
}
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M. Sh. Shabozov; Kh. M. Khuromonov. On the best approximation in the mean of functions of a complex variable by Fourier series in the Bergman space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2020), pp. 74-92. http://geodesic.mathdoc.fr/item/IVM_2020_2_a6/