90
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Zolotarev's conformal mapping and Chebotarev's problem

References

  • Pólya G. Beitrag zur Verallgemeinerung des Verzerrungssatzes auf mehrfach zusammenhängende Gebiete. III Sitzungsberichte Preuss. Akad Wiss Berlin Phys Math Kl. 1929;55–62. (in German).
  • Grötzsch H. Über ein Variationsproblem der konformen Abbildung. Berichte Leipzig. 1930;82:251–263. (in German).
  • Lavrentiev MA. On the theory of conformal mappings. Trudy Fiz Mat Inst Steklov. 1934;5:159–245. Russian; english translation in ‘Ten papers on complex analysis’, American Mathematical Society Translations, Series 2, Vol. 122 (1984), p. 1–64).
  • Grassmann EG, Rokne J. An explicit calculation of some sets of minimal capacity. SIAM J Math Anal. 1975;6:242–249. doi: 10.1137/0506024
  • Grassmann E, Rokne J. Calculation of some extremal conformal mappings. SIAM J Math Anal. 1978;9:87–105. doi: 10.1137/0509008
  • Nuttall J, Singh SR. Orthogonal polynomials and Padé approximants associated with a system of arcs. J Approx Theory. 1977;21:1–42. doi: 10.1016/0021-9045(77)90117-4
  • Ransford T. Potential theory in the complex plane. Cambridge: Cambridge University Press; 1995.
  • Ransford T. Computation of logarithmic capacity. Comput Methods Funct Theory. 2010;10:555–578. doi: 10.1007/BF03321780
  • Schiefermayr K. Chebotarev's problem and inverse polynomial images. Acta Math Hungar. 2014;214:80–94. doi: 10.1007/s10474-013-0353-5
  • Jenkins JA. On certain geometrical problems associated with capacity. Math Nachr. 1969;39:349–356. doi: 10.1002/mana.19690390412
  • Zolotarev EI. Sur la méthode d'integration de M. Tchebichef J Math Pures Appl. 1874;19:161–188. (in French).
  • Achieser NI. Über einige Funktionen, die in gegebenen Intervallen am wenigsten von Null abweichen. Bull Phys Math Kasan Ser III. 1929;3:1–69. (in German).
  • Achieser NI. Über einige Funktionen, welche in zwei gegebenen Intervallen am wenigsten von Null abweichen. Bull Acad Sci URSS. 1932;7:1163–1202. (in German).
  • Peherstorfer F, Schiefermayr K. Description of inverse polynomial images which consist of two Jordan arcs with the help of Jacobi's elliptic functions. Comput Methods Funct Theory. 2004;4:355–390. doi: 10.1007/BF03321075
  • Kuzmina GV. Moduli of families of curves and quadratic differentials. Proc Steklov Inst Math. 1982;139:1–231.
  • Kuzmina GV. Methods of the geometric theory of functions. I. St Petersburg Math J. 1998;9:455–507.
  • Kuzmina GV. Methods of the geometric theory of functions. II. St Petersburg Math J. 1998;9:889–930.
  • Fedorov SI. Chebotarev's variational problem in the theory of the capacity of plane sets and covering theorems for univalent conformal mappings. Math USSR Sb. 1985;52:115–133. doi: 10.1070/SM1985v052n01ABEH002880
  • Lawden DF. Elliptic functions and applications. New York: Springer; 1989.
  • Schiefermayr K. A density result concerning inverse polynomial images. Proc Amer Math Soc. 2014;142:539–545. doi: 10.1090/S0002-9939-2013-11770-3
  • Pirl U. Über die geometrische Gestalt eines Extremalkontinuums aus der Theorie der konformen Abbildung. Math Nachr. 1969;39:297–312. (in German). doi: 10.1002/mana.19690390408
  • Schiefermayr K. Inverse polynomial images consisting of an interval and an arc. Comput Methods Funct Theory. 2009;9:407–420. doi: 10.1007/BF03321736
  • Byrd PF, Friedman MD. Handbook of elliptic integrals for engineers and scientists. Berlin: Springer; 1971.
  • Carlson BC, Todd J. The degenerating behaviour of elliptic functions. SIAM J Numer Anal. 1983;20:1120–1129. doi: 10.1137/0720081
  • Whittaker ET, Watson GN. A course of modern analysis. Cambridge: Cambridge University Press; 1962.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.