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On the rate of rational approximation of functions on tangent continua

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Abstract

Upper and lower bounds are established for the rate of rational approximation of functions piecewise analytic on tangent continua. In some special cases, these bounds are coordinated depending on the mutual location of the continua.

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References

  1. D. J. Newman, “Rational approximation to ¦x¦,”Mick. Math. J.,11, No. 1, 11–14 (1964).

    Google Scholar 

  2. P. Turan, “On approximation of piecewise analytic functions by rational functions,” in:Modern Problems of the Theory of Analytic Functions [in Russian], Nauka, Moscow (1966), pp. 296–300.

    Google Scholar 

  3. A. A. Gonchar, “Estimates of growth of rational functions and some applications,”Mat. Sb.,72, No. 3, 489–503 (1967).

    Google Scholar 

  4. A. A. Gonchar, “The rate of rational approximation and univalence property of an analytic function in a neighborhood of an isolated singular point,”Mat. Sb.,94, No. 2, 265–283 (1974).

    Google Scholar 

  5. I. I. Mikaelyan, “On the best approximations by rational functions in tangent domains,”Dokl. Akad. Nauk Arm. SSR,57, No. 3, 134–139 (1973).

    Google Scholar 

  6. G. David, “Operateurs integraux singuliers sur certain courbes du plan complexe,”Ann. Sci. Ecole Norm. Super.,17, 157–189 (1984).

    Google Scholar 

  7. O. Martio and J. Sarvas, “Injectivity theorems in plane and space,”Ann. Acad. Sci. Fenn. Ser. AI Math.,4, 383–401 (1978–1979).

    Google Scholar 

  8. E. Johnston, “Growth of derivatives and the modulus of continuity of analytic functions,”Rocky Mount. J. Math.,9, No. 4, 671–682 (1979).

    Google Scholar 

  9. V. K. Dzyadyk,Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  10. V. V. Maimeskul, “Estimates of growth of conjugate harmonic polynomials in domains of complex plane,”Ukr. Mat. Zh.,42, No. 6, 772–777 (1990).

    Google Scholar 

  11. E. M. Stein,Singular Integrals and Differentiability Properties of Functions, Princeton University Press. Princeton, N.J. (1970).

    Google Scholar 

  12. A. A. Gonchar, “The rate of approximation by rational fractions and function properties,” in:Proceedings of the International Congress of Mathematicians [Russian translation], Mir, Moscow (1968), pp. 329–356.

    Google Scholar 

  13. L. Ahlfors,Conformal Invariants. Topics in Geometric Function Theory, McGraw-Hill, New York (1973).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk

    V. V. Maimeskul

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  1. V. V. Maimeskul
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 11, pp. 1522–1533, November, 1993.

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Maimeskul, V.V. On the rate of rational approximation of functions on tangent continua. Ukr Math J 45, 1713–1726 (1993). https://doi.org/10.1007/BF01060861

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  • DOI: https://doi.org/10.1007/BF01060861

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