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

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Distance estimates and pointwise bounded density

Authors: A. M. Davie, T. W. Gamelin and J. Garnett
Journal: Trans. Amer. Math. Soc. 175 (1973), 37-68
MSC: Primary 30A78; Secondary 30A98, 46J15
MathSciNet review: 0313514
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let U be a bounded open subset of the complex plane, and let H be a closed subalgebra of $ {H^\infty }(U)$, the bounded analytic functions on U. If E is a subset of $ \partial U$, let $ {L_E}$ be the algebra of all bounded continuous functions on U which extend continuously to E, and set $ {H_E} = H \cap {L_E}$. This paper relates distance estimates of the form $ d(h,H) = d(h,{H_E})$, for all $ h \in {L_E}$, to pointwise bounded density of $ {H_E}$ in H. There is also a discussion of the linear space $ H + {L_E}$, which turns out often to be a closed algebra.

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30A78, 30A98, 46J15

Retrieve articles in all journals with MSC: 30A78, 30A98, 46J15

Additional Information

PII: S 0002-9947(1973)0313514-8
Keywords: Bounded analytic functions, pointwise bounded approximation, uniform approximation, distance estimates
Article copyright: © Copyright 1973 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