On an equivalent definition of the transfinite diameter

@inproceedings{Davis1952OnAE,
  title={On an equivalent definition of the transfinite diameter},
  author={Philip J. Davis and Henry O. Pollak},
  year={1952}
}
(1) f(v) = aL + ao + ail/ + * ,a > 0, map the exterior of the unit circle C onto the exterior of a simplyconnected domain B. It is part of a general theory (see e.g. [3 ]) that the quantity 1/a can be identified with the transfinite diameter of B. In particular, let Tn(z) be the polynomial of degree n with leading coefficient 1 whose LX norm over B, i.e. the maximum of whose absolute value over B, is minimum. Then lim (M>)"n = a. 

Citations

Publications citing this paper.

Asymptotic behavior of restricted extremal polynomials and of their zeros

VIEW 10 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

References

Publications referenced by this paper.
SHOWING 1-2 OF 2 REFERENCES

Ueber die Approximation analytischer Funktionen durch lineare Aggregate von vorgegebenen Potenzen

  • T. Carleman
  • Archiv foer Mathematik, Astronomi och Fysik vol
  • 1922
VIEW 1 EXCERPT