A Note on Projective Capacity

Author:

Alexander H.

Abstract

Introduction. In [1] we defined a capacity in Cn. Recently Molzon, Shiffman and Sibony [8] have introduced a different capacity which is useful for certain Bezout estimates. The object of this note is to apply the methods of [1] to study the capacity of [8]. We shall obtain an equivalent definition of this capacity via Tchebycheff polynomials, along the lines of [1]. Half of this equivalence was independently obtained by Sibony [9].To establish the full equivalence of these two approaches to capacity a notion of Jensen measures in a setting more general than uniform algebras is needed. We shall consider Jensen measures for multiplicative semigroups; these are sets of functions in which only the multiplicative structure is postulated. It will also be useful to generalize the notion of polynomial hull in Cn to a hull with respect to a multiplicative semigroup of polynomials. We can then adapt the approach of [1] to these semigroups.

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Some applications of projective logarithmic potentials;Journal of Mathematical Analysis and Applications;2022-02

2. Transfinite diameter, Chebyshev constants, and capacities in Cn;Annales Polonici Mathematici;2012

3. Croissance de la trace d'un courant positif fermé sur les plans complexes de Cn;Journal de Mathématiques Pures et Appliquées;2005-02

4. Comparison of two capacities in ? n;Mathematische Zeitschrift;1984-09

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