Abstract:
In the paper inequalities containing discrete and uniform norms of polynomials on an interval and a circle arc are proved. The proofs are based on Bernstein-type inequalities. Obtained inequalities supplement some corresponding results of Rakhmanov, Shekhtman, Sheil-Small, Dubinin.
Key words and phrases:
discrete and uniform norms of polynomials, Bernstein-type inequalities.
Citation:
S. I. Kalmykov, “Comparison of discrete and uniform norms of polynomials on a segment and a circle arc”, Analytical theory of numbers and theory of functions. Part 27, Zap. Nauchn. Sem. POMI, 404, POMI, St. Petersburg, 2012, 175–183; J. Math. Sci. (N. Y.), 193:1 (2013), 100–105
\Bibitem{Kal12}
\by S.~I.~Kalmykov
\paper Comparison of discrete and uniform norms of polynomials on a~segment and a~circle arc
\inbook Analytical theory of numbers and theory of functions. Part~27
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 404
\pages 175--183
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5266}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3029599}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 193
\issue 1
\pages 100--105
\crossref{https://doi.org/10.1007/s10958-013-1437-z}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884974534}
Linking options:
https://www.mathnet.ru/eng/znsl5266
https://www.mathnet.ru/eng/znsl/v404/p175
This publication is cited in the following 1 articles:
Michael I. Ganzburg, “Discretization Theorems for Entire Functions of Exponential Type”, Journal of Mathematical Analysis and Applications, 2025, 129510
Citation in format AMSBIB
Contact us: