Abstract:
We give a characterization of elements of a subspace of a complex Banach space with the property that the norm of a bounded linear functional on the subspace is attained at those elements. In particular, we discuss properties of polynomials that are extremal in sharp pointwise Nikol'skii inequalities for algebraic polynomials in a weighted Lq-space on a finite or infinite interval.
Keywords:
Complex Banach space, Bounded linear functional on a subspace, Algebraic polynomial, Pointwise Nikol'skii inequality.
\Bibitem{Are17}
\by Vitalii~V.~Arestov
\paper A characterization of extremal elements in some linear problems
\jour Ural Math. J.
\yr 2017
\vol 3
\issue 2
\pages 22--32
\mathnet{http://mi.mathnet.ru/umj39}
\crossref{https://doi.org/10.15826/umj.2017.2.004}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR3746948}
\elib{https://elibrary.ru/item.asp?id=32334095}
Linking options:
https://www.mathnet.ru/eng/umj39
https://www.mathnet.ru/eng/umj/v3/i2/p22
This publication is cited in the following 4 articles:
V. V. Arestov, M. V. Deikalova, “A Generalized Translation Operator Generated by the Sinc Function on an Interval”, Proc. Steklov Inst. Math. (Suppl.), 323, suppl. 1 (2023), S32–S52
V. V. Arestov, M. V. Deikalova, “On One Generalized Translation and the Corresponding Inequality of Different Metrics”, Proc. Steklov Inst. Math. (Suppl.), 319, suppl. 1 (2022), S30–S42
Vitalii V. Arestov, Marina V. Deikalova, “On one inequality of different metrics for trigonometric polynomials”, Ural Math. J., 8:2 (2022), 27–45
V. Arestov, A. Babenko, M. Deikalova, Á. Horváth, “Nikol'skii Inequality Between the Uniform Norm and Integral Norm with Bessel Weight for Entire Functions of Exponential Type on the Half-Line”, Anal Math, 44:1 (2018), 21
Citation in format AMSBIB
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