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

Year 2012, Volume: 33 Issue: 2, 32 - 45, 21.02.2013

F.g. Abdullayev , N.d. Aral

Abstract

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

Keywords

Algebraic polynomials conformal mapping quasiconformal mapping quasiconformal curve

References

  • 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.

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

Year 2012, Volume: 33 Issue: 2, 32 - 45, 21.02.2013

F.g. Abdullayev , N.d. Aral

Abstract

References

  • 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.
There are 12 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Editorial
Authors

F.g. Abdullayev

N.d. Aral This is me

Publication Date February 21, 2013
Published in Issue Year 2012 Volume: 33 Issue: 2

Cite

APA Abdullayev, F., & Aral, N. (2013). ON THE POINTWISE GROWTH OF POLYNOMIALS IN UNBOUNDED REGIONS WITH QUASICONFORMAL BOUNDARY. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, 33(2), 32-45.
AMA Abdullayev F, Aral N. ON THE POINTWISE GROWTH OF POLYNOMIALS IN UNBOUNDED REGIONS WITH QUASICONFORMAL BOUNDARY. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. February 2013;33(2):32-45.
Chicago Abdullayev, F.g., and N.d. Aral. “ON THE POINTWISE GROWTH OF POLYNOMIALS IN UNBOUNDED REGIONS WITH QUASICONFORMAL BOUNDARY”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 33, no. 2 (February 2013): 32-45.
EndNote Abdullayev F, Aral N (February 1, 2013) ON THE POINTWISE GROWTH OF POLYNOMIALS IN UNBOUNDED REGIONS WITH QUASICONFORMAL BOUNDARY. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 33 2 32–45.
IEEE F. Abdullayev and N. Aral, “ON THE POINTWISE GROWTH OF POLYNOMIALS IN UNBOUNDED REGIONS WITH QUASICONFORMAL BOUNDARY”, Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 33, no. 2, pp. 32–45, 2013.
ISNAD Abdullayev, F.g. - Aral, N.d. “ON THE POINTWISE GROWTH OF POLYNOMIALS IN UNBOUNDED REGIONS WITH QUASICONFORMAL BOUNDARY”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 33/2 (February 2013), 32-45.
JAMA Abdullayev F, Aral N. ON THE POINTWISE GROWTH OF POLYNOMIALS IN UNBOUNDED REGIONS WITH QUASICONFORMAL BOUNDARY. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2013;33:32–45.
MLA Abdullayev, F.g. and N.d. Aral. “ON THE POINTWISE GROWTH OF POLYNOMIALS IN UNBOUNDED REGIONS WITH QUASICONFORMAL BOUNDARY”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 33, no. 2, 2013, pp. 32-45.
Vancouver Abdullayev F, Aral N. ON THE POINTWISE GROWTH OF POLYNOMIALS IN UNBOUNDED REGIONS WITH QUASICONFORMAL BOUNDARY. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2013;33(2):32-45.