Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the local asymptotics of Faber polynomials
HTML articles powered by AMS MathViewer

by Igor E. Pritsker PDF
Proc. Amer. Math. Soc. 127 (1999), 2953-2960 Request permission

Abstract:

We study a local asymptotics of the (generalized) Faber polynomials at the boundary of the associated domain, under certain mild smoothness conditions on the weight function and geometric conditions on the boundary. The main result exhibits how this asymptotics depends on the corners at the boundary. Its proof is based on the continuity properties of the Visser-Ostrowski quotient at the corners.
References
  • Saunders MacLane, Steinitz field towers for modular fields, Trans. Amer. Math. Soc. 46 (1939), 23–45. MR 17, DOI 10.1090/S0002-9947-1939-0000017-3
  • J. H. Curtiss, Faber polynomials and the Faber series, Amer. Math. Monthly 78 (1971), 577–596. MR 293104, DOI 10.2307/2316567
  • Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
  • R. E. Edwards, Fourier series. A modern introduction. Vol. 1, 2nd ed., Graduate Texts in Mathematics, vol. 64, Springer-Verlag, New York-Berlin, 1979. MR 545506, DOI 10.1007/978-1-4612-6208-4
  • G. Faber, Über polynomische Entwicklungen, Math. Ann. 57 (1903), 389–408.
  • G. Faber, Über polynomische Entwicklungen II, Math. Ann. 64 (1907), 116–135.
  • G. Faber, Über Tschebyscheffsche Polynome, J. Reine Angew. Math. 150 (1920), 79–106.
  • D. GaÄ­er, Lektsii po teorii approksimatsii v kompleksnoÄ­ oblasti, “Mir”, Moscow, 1986 (Russian). Translated from the German by L. M. Kartashov; Translation edited and with a preface by V. I. BelyÄ­ and P. M. Tamrazov. MR 894919
  • Morgan Ward and R. P. Dilworth, The lattice theory of ova, Ann. of Math. (2) 40 (1939), 600–608. MR 11, DOI 10.2307/1968944
  • G. G. Lorentz, Approximation of functions, 2nd ed., Chelsea Publishing Co., New York, 1986. MR 917270
  • Ch. Pommerenke, Boundary behaviour of conformal maps, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 299, Springer-Verlag, Berlin, 1992. MR 1217706, DOI 10.1007/978-3-662-02770-7
  • Ch. Pommerenke, Über die Faberschen Polynome schlichter Funktionen, Math. Z. 85 (1964), 197–208 (German). MR 168772, DOI 10.1007/BF01112141
  • V. I. Smirnov and N. A. Lebedev, Functions of a complex variable: Constructive theory, The M.I.T. Press, Cambridge, Mass., 1968. Translated from the Russian by Scripta Technica Ltd. MR 0229803
  • P. K. Suetin, V. A. Steklov’s problem in the theory of orthogonal polynomials, J. Soviet Math. 12 (1979), 631–682.
  • P. K. Suetin, Mnogochleny, ortogonal′nye po ploshchadi, i mnogochleny Bieberbakha, Izdat. “Nauka”, Moscow, 1971 (Russian). Trudy Mat. Inst. Steklov. 100 (1971). MR 0463792
  • P. K. Suetin, Series in Faber Polynomials, Nauka, Moscow, 1984. (in Russian)
  • GĂĄbor Szegő, Orthogonal polynomials, 4th ed., American Mathematical Society Colloquium Publications, Vol. XXIII, American Mathematical Society, Providence, R.I., 1975. MR 0372517
  • H. Widom, Extremal polynomials associated with a system of curves in the complex plane, Adv. Math. 3 (1969), 127–232.
Similar Articles
Additional Information
  • Igor E. Pritsker
  • MR Author ID: 319712
  • Email: iep@po.cwru.edu
  • Received by editor(s): November 4, 1997
  • Received by editor(s) in revised form: December 31, 1997
  • Published electronically: April 23, 1999
  • Additional Notes: Research supported in part by the National Science Foundation grant DMS-9707359.

    • Dedicated: Dedicated to Professor D. Gaier on the occasion of his seventieth birthday.
  • Communicated by: Albert Baernstein II
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 2953-2960
  • MSC (1991): Primary 30C10, 30E15; Secondary 30E10, 30C35
  • DOI: https://doi.org/10.1090/S0002-9939-99-04891-1
  • MathSciNet review: 1605937