Orthogonal Measures on the Boundary of a Riemann Surface and Polynomial Hull of Compacts of Finite Length
✍ Scribed by Tien-Cuong Dinh
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 427 KB
- Volume
- 157
- Category
- Article
- ISSN
- 0022-1236
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✦ Synopsis
Let + be an orthogonal measure with compact support of finite length in C n . We prove, under a very weak hypothesis of regularity on the support (Supp +) of +, that this measure is characterized by its boundary values (in the weak sense of currents) of the current [T] 7 ., where T is an analytic subset of dimension 1 of C n "Supp + and . is a holomorphic (1, 0)-form on T. This allows us to prove that the polynomial hull X of a compactum X/C n of finite length with a weak regularity assumption is its union with an analytic subset of pure dimension 1 of C n "X. We also prove that the measure + can be decomposed into a sum of orthogonal measures will small support. We deduce that a continuous function on X is approximable by polynomials if and only if it is locally approximable.
1998 Academic Press Alexander [2]. In a special class, denoted A 1 , X "X is an analytic subset of C n "X and, moreover in C n this subset defines a current of bidimension (1, 1) of finite mass whose boundary is a rectifiable current having its support in X article no.