Abstract:
A connection is established between uniform rational approximation, and approximation in the mean by polynomials on compact nowhere dense subsets of the complex plane C. Peak points for R(X) and bounded point evaluations for Hp(X,dA), 1≤p<∞, play a fundamental role.
Keywords:
polynomial and rational approximation, capacity, peak points, point evaluations.
Citation:
J. E. Brennan, E. R. Militzer, “Lp-bounded point evaluations for polynomials and uniform rational approximation”, Algebra i Analiz, 22:1 (2010), 57–74; St. Petersburg Math. J., 22:1 (2011), 41–53
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\by J.~E.~Brennan, E.~R.~Militzer
\paper $L^p$-bounded point evaluations for polynomials and uniform rational approximation
\jour Algebra i Analiz
\yr 2010
\vol 22
\issue 1
\pages 57--74
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\transl
\jour St. Petersburg Math. J.
\yr 2011
\vol 22
\issue 1
\pages 41--53
\crossref{https://doi.org/10.1090/S1061-0022-2010-01131-2}
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Linking options:
https://www.mathnet.ru/eng/aa1170
https://www.mathnet.ru/eng/aa/v22/i1/p57
This publication is cited in the following 6 articles:
Yang L., “Bounded Point Evaluations For Certain Polynomial and Rational Modules”, J. Math. Anal. Appl., 474:1 (2019), 219–241
Yang L., “Spectral Picture For Rationally Multicyclic Subnormal Operators”, Banach J. Math. Anal., 13:1 (2019), 151–173
Yang L., “Bounded Point Evaluations For Rationally Multicyclic Subnormal Operators”, J. Math. Anal. Appl., 458:2 (2018), 1059–1072
Yang L., “A note on $L^p$-bounded point evaluations for polynomials”, Proc. Amer. Math. Soc., 144:11 (2016), 4943–4948
Brennan J.E., “Absolutely Continuous Representing Measures For $R(X)$”, Bull. London Math. Soc., 46:6 (2014), 1133–1144
J. E. Brennan, C. N. Mattingly, “Approximation by rational functions on compact nowhere dense subsets of the complex plane”, Anal.Math.Phys., 3:3 (2013), 201
Citation in format AMSBIB
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