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A Note on Projective Capacity

Published online by Cambridge University Press:  20 November 2018

H. Alexander
H. Alexander*
Affiliation:
University of Illinois, Chicago, Illinois
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 6 , 01 December 1982 , pp. 1319 - 1329
Copyright
Copyright © Canadian Mathematical Society 1982

References

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