منابع مشابه
Transfinite Diameter
The transfinite diameter is a way of quantifying the size of compact sets in Euclidean space. This quantity is related to the Hausdorff dimension and the Lebesgue measure, but gives a slightly different perspective on the set than either of those do. In this paper, we introduce the transfinite diameter, and outline some attempts to calculate this quantity for three sets in R. For z1, z2, . . . ...
متن کاملThe monic integer transfinite diameter
We study the problem of finding nonconstant monic integer polynomials, normalized by their degree, with small supremum on an interval I. The monic integer transfinite diameter tM(I) is defined as the infimum of all such supremums. We show that if I has length 1, then tM(I) = 1 2 . We make three general conjectures relating to the value of tM(I) for intervals I of length less than 4. We also con...
متن کاملTransfinite Diameter and the Resultant
We prove a formula for the Fekete-Leja transfinite diameter of the pullback of a set E ⊂ C by a regular polynomial map F , expressing it in terms of the resultant of the leading part of F and the transfinite diameter of E. We also establish the nonarchimedean analogue of this formula. A key step in the proof is a formula for the transfinite diameter of the filled Julia set of F .
متن کاملOn an Equivalent Definition of the Transfinite Diameter
PHILIP DAVIS AND HENRY POLLAK Let (1) /(f) = af + a0 + ai/l + ■ ■ ■ , 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 L°° norm over B, i.e. t...
متن کاملA Robin formula for the Fekete-Leja transfinite diameter
We generalize the classical Robin formula to higher dimensions. Mathematics Subject Classification (2000) Primary 32U35 · 32U20 · 14G40; Secondary 31B15 · 31C10 The purpose of this note is to give a formula for the Fekete-Leja transfinite diameter on CN , generalizing the classical Robin formula d∞(E) = e−V(E) for the usual transfinite diameter. We will disengage this from a formula for the sec...
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ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 1999
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap-72-3-285-305