Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On interpolating functions with minimal norm


Authors: A. Stray and K. O. Øyma
Journal: Proc. Amer. Math. Soc. 68 (1978), 75-78
MSC: Primary 30A80
DOI: https://doi.org/10.1090/S0002-9939-1978-0457734-0
MathSciNet review: 0457734
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {H^\infty }$ denote the Banach algebra of bounded analytic functions in the unit disc $ \{ z:\vert z\vert < 1\} $. If f is an extreme point in the unit ball of $ {H^\infty }$, there is always a Blaschke product B, whose zeros form an interpolating sequence tending to one point of the unit circle, such that $ {\left\Vert {f + Bh} \right\Vert _\infty } > 1$ if $ h \in {H^\infty }$ and $ h \ne 0$. An application of this result to the theory of best approximation is given.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30A80

Retrieve articles in all journals with MSC: 30A80


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0457734-0
Keywords: Minimal interpolating function, best approximation
Article copyright: © Copyright 1978 American Mathematical Society