Geodesic
The Gelfand and Bernstein widths of some classes of analytic functions.~II
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 24, Tome 232 (1996), pp. 134-140

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The Gelfand widths of the unit ball of $H^2(\nu)$ (the weighted Hardy space) with respect to the metric of the space $L_\infty(T_r)$ are considered ($T_r$ being the circle of radius $r$ centered at the origin), as well as the Bernstein widths of the unit ball of $H^\infty$ with respect to the metric of the space $L_2(T_r,\mu)$. The asymptotic formulas for the widths in the question are established for arbitrary measures $\nu,\mu$. Bibl. 5 titles. 
@article{ZNSL_1996_232_a10,
     author = {O. G. Parfenov},
     title = {The {Gelfand} and {Bernstein} widths of some classes of analytic {functions.~II}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {134--140},
     publisher = {mathdoc},
     volume = {232},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_232_a10/}
}
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O. G. Parfenov. The Gelfand and Bernstein widths of some classes of analytic functions.~II. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 24, Tome 232 (1996), pp. 134-140. http://geodesic.mathdoc.fr/item/ZNSL_1996_232_a10/