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.
Similar content being viewed by others
References
D. J. Newman, “Rational approximation to ¦x¦,”Mick. Math. J.,11, No. 1, 11–14 (1964).
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.
A. A. Gonchar, “Estimates of growth of rational functions and some applications,”Mat. Sb.,72, No. 3, 489–503 (1967).
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).
I. I. Mikaelyan, “On the best approximations by rational functions in tangent domains,”Dokl. Akad. Nauk Arm. SSR,57, No. 3, 134–139 (1973).
G. David, “Operateurs integraux singuliers sur certain courbes du plan complexe,”Ann. Sci. Ecole Norm. Super.,17, 157–189 (1984).
O. Martio and J. Sarvas, “Injectivity theorems in plane and space,”Ann. Acad. Sci. Fenn. Ser. AI Math.,4, 383–401 (1978–1979).
E. Johnston, “Growth of derivatives and the modulus of continuity of analytic functions,”Rocky Mount. J. Math.,9, No. 4, 671–682 (1979).
V. K. Dzyadyk,Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow (1977).
V. V. Maimeskul, “Estimates of growth of conjugate harmonic polynomials in domains of complex plane,”Ukr. Mat. Zh.,42, No. 6, 772–777 (1990).
E. M. Stein,Singular Integrals and Differentiability Properties of Functions, Princeton University Press. Princeton, N.J. (1970).
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.
L. Ahlfors,Conformal Invariants. Topics in Geometric Function Theory, McGraw-Hill, New York (1973).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 11, pp. 1522–1533, November, 1993.
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01060861