Abstract:
A lower bound is derived for the maximum value of the minimum modulus of an analytic function on a circle whose radius runs through an interval with a fixed ratio of endpoints.
Keywords:
analytic function, entire function, minimum modulus, maximum modulus.
This work was supported by the Russian Science Foundation under grant no. 22-21-00545, https://rscf.ru/project/22-21-00545/, and performed at the Lomonosov Moscow State University.
Citation:
A. Yu. Popov, “Lower Bound on the Minimum Modulus of an Analytic Function on a Circle in Terms of a Negative Power of Its Norm on a Larger Circle”, Approximation Theory, Functional Analysis, and Applications, Collected papers. On the occasion of the 70th birthday of Academician Boris Sergeevich Kashin, Trudy Mat. Inst. Steklova, 319, Steklov Math. Inst., Moscow, 2022, 223–250; Proc. Steklov Inst. Math., 319 (2022), 209–236
\Bibitem{Pop22}
\by A.~Yu.~Popov
\paper Lower Bound on the Minimum Modulus of an Analytic Function on a Circle in Terms of a Negative Power of Its Norm on a Larger Circle
\inbook Approximation Theory, Functional Analysis, and Applications
\bookinfo Collected papers. On the occasion of the 70th birthday of Academician Boris Sergeevich Kashin
\serial Trudy Mat. Inst. Steklova
\yr 2022
\vol 319
\pages 223--250
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4257}
\crossref{https://doi.org/10.4213/tm4257}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2022
\vol 319
\pages 209--236
\crossref{https://doi.org/10.1134/S0081543822050157}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85148428450}
Linking options:
https://www.mathnet.ru/eng/tm4257
https://doi.org/10.4213/tm4257
https://www.mathnet.ru/eng/tm/v319/p223
This publication is cited in the following 3 articles:
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