Abstract:
It is shown that a well-known expression for the capacity of the preimage of a compact set under a polynomial map remains valid in the case of a rational map, provided that the standard capacity of the preimage is replaced by its capacity in the external field determined by the poles in C of the rational function determining the map.
This work was supported in part by the program
“Modern Problems of Theoretical Mathematics” of Branch of Mathematics,
Russian Academy of Sciences,
by the Russian Foundation for Basic Research
under grant 15-01-07531,
and by the program “Leading Scientific Schools”
under grant NSh-9110.2016.1.
Citation:
V. I. Buslaev, “The Capacity of the Rational Preimage of a Compact Set”, Mat. Zametki, 100:6 (2016), 790–799; Math. Notes, 100:6 (2016), 781–790
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Linking options:
https://www.mathnet.ru/eng/mzm11279
https://doi.org/10.4213/mzm11279
https://www.mathnet.ru/eng/mzm/v100/i6/p790
This publication is cited in the following 8 articles:
V. I. Buslaev, “On a lower bound for the rate of convergence of multipoint Padé approximants of piecewise analytic functions”, Izv. Math., 85:3 (2021), 351–366
V. I. Buslaev, “Convergence of a Limit Periodic Schur Continued Fraction”, Math. Notes, 107:5 (2020), 701–712
V. I. Buslaev, “Schur's Criterion for Formal Newton Series”, Math. Notes, 108:6 (2020), 884–888
V. I. Buslaev, “Necessary and sufficient conditions for extending a function to a Schur function”, Sb. Math., 211:12 (2020), 1660–1703
V. I. Buslaev, “Continued fractions with limit periodic coefficients”, Sb. Math., 209:2 (2018), 187–205
V. I. Buslaev, “On Singular points of Meromorphic Functions Determined by Continued Fractions”, Math. Notes, 103:4 (2018), 527–536
M. Ya. Mazalov, “On Bianalytic Capacities”, Math. Notes, 103:4 (2018), 672–677
V. I. Buslaev, “On the Van Vleck Theorem for Limit-Periodic Continued Fractions of General Form”, Proc. Steklov Inst. Math., 298 (2017), 68–93
Citation in format AMSBIB
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