Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Tame measures on certain compact sets

Author: Hsuan Pei Lee
Journal: Proc. Amer. Math. Soc. 80 (1980), 61-67
MSC: Primary 46J10; Secondary 46E27
MathSciNet review: 574509
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A finite complex Borel measure $ \mu $ on a compact subset $ X \subset {{\mathbf{C}}^n}$ is called tame if there exist finite measures $ {\sigma _1}, \ldots ,{\sigma _n}$ on X with

$\displaystyle \int_X \phi d\mu = \int_X {\sum\limits_1^n {\frac{{\partial \phi }}{{\partial {{\bar z}_j}}}d{\sigma _j}} } $

for every $ \phi \in C_0^\infty ({{\mathbf{C}}^n})$. We define $ {X_T} = \{ ({z_1},{z_2}):\vert{z_1}{\vert^2} + \vert{z_2}{\vert^2} = 1$ and $ {z_1} \in T\} $, where T is a compact subset of $ \{ \vert{z_1}\vert < 1\} $ in $ {{\mathbf{C}}^1}$. It is shown in this paper that tame measures form a weak-$ ^ \ast $ dense subset of $ R{({X_T})^ \bot }$. It follows then, with the help of a theorem by Weinstock, that $ R({X_T})$ is a local algebra.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46J10, 46E27

Retrieve articles in all journals with MSC: 46J10, 46E27

Additional Information

PII: S 0002-9939(1980)0574509-1
Keywords: Tame measure, weak-$ ^ \ast $ dense, local algebra
Article copyright: © Copyright 1980 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia