ON THE POINTWISE GROWTH OF POLYNOMIALS IN UNBOUNDED REGIONS WITH QUASICONFORMAL BOUNDARY

ON THE POINTWISE GROWTH OF POLYNOMIALS IN UNBOUNDED REGIONS WITH QUASICONFORMAL BOUNDARY

In this present work, we continue studying the estimation of Bernstein-Walsh type for algebraic polynomials in the regions with quasiconformal boundary.

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  • Abdullayev F.G., Dissertation (Ph.D.), Donetsk, 1986, 120 p.
  • Abdullayev F.G., Uniform Convergence of Generalized Bieberbach Polynomials in Re- gions with non-zero angles, Acta Mathematica Hungarica, 1997, 77, 3, 223-246.
  • Abdullayev F.G., On the some properties of the orthogonal polynomials over the region of the complex plane (Part III), Ukr.Math.J., 2001, Vol.53, No:12, pp.1934-1948.
  • Abdullayev F.G., The properties of the orthogonal polynomials with weight having singulerity on the boundary contour, J. of Comp. Anal. and Appl. , 2004, Vol.6, No: 1, pp. 43-59.
  • Ahlfors L.V., Lectures on Quasiconformal Mappings, Van Nostrand (Prinston, NJ, 1966).
  • Andrievskii V.V., Constructive characterization of the harmonic functions in domains with quasiconformal boundary, In: Quasiconformal continuation and Approximation by function in the set of the complex plane. Kiev, 1985 [in Russian]
  • Andrievskii V.V., Belyi V.I.& Dzyadyk V.K, Conformal invariants in constructive theory of functions of complex plane. Atlanta:World Federation Publ.Com., 1995.
  • Lehto O., Virtanen K.I., Quasiconformal Mapping in the Plane, Springer Verlag, Berlin, 1973.
  • Rickman S., Characterisation of quasiconformal arcs, Ann. Acad. Sci. Fenn., Ser. A, Mathematica., 1966, 395 , 30 p.
  • Stylianopoulos N., Fine asymptotics for Bergman orthogonal polynomials over do- mains with corners, CMFT 2009, Ankara, June 2009.
  • Hille E., Szeg¨o G., Tamarkin J.D., On some generalization of a theorem of A.Markoff , Duke Math., 1937, 3, p. 729-739.
  • Walsh J.L., Interpolation and Approximation by Rational Functions in the Complex Domain, AMS,1960.