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Zapiski Nauchnykh Seminarov POMI, 1996, Volume 232, Pages 134–140 (Mi znsl3682)  

The Gelfand and Bernstein widths of some classes of analytic functions. II

O. G. Parfenov

Pskov State Pedagogical Institute
Abstract: 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.
Received: 13.11.1995
English version:
Journal of Mathematical Sciences (New York), 1998, Volume 92, Issue 1, Pages 3630–3634
DOI: https://doi.org/10.1007/BF02440148
Bibliographic databases:
Document Type: Article
UDC: 517.43+517.51
Language: Russian
Citation: O. G. Parfenov, “The Gelfand and Bernstein widths of some classes of analytic functions. II”, Investigations on linear operators and function theory. Part 24, Zap. Nauchn. Sem. POMI, 232, POMI, St. Petersburg, 1996, 134–140; J. Math. Sci. (New York), 92:1 (1998), 3630–3634
Citation in format AMSBIB
\Bibitem{Par96}
\by O.~G.~Parfenov
\paper The Gelfand and Bernstein widths of some classes of analytic functions.~II
\inbook Investigations on linear operators and function theory. Part~24
\serial Zap. Nauchn. Sem. POMI
\yr 1996
\vol 232
\pages 134--140
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3682}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1464430}
\zmath{https://zbmath.org/?q=an:0907.41021|0889.41019}
\transl
\jour J. Math. Sci. (New York)
\yr 1998
\vol 92
\issue 1
\pages 3630--3634
\crossref{https://doi.org/10.1007/BF02440148}
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