Abstract
The value of an analytic function at the center of a disc is equal to its average over the disc. This implies that evaluation at a point of D is a bounded linear functional on A2(D), and hence that Cauchy sequences in the norm are Cauchy sequences in the sense of uniform convergence on compact sets.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Rights and permissions
Copyright information
© 1982 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Halmos, P.R. (1982). Analytic Functions. In: A Hilbert Space Problem Book. Graduate Texts in Mathematics, vol 19. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9330-6_29
Download citation
DOI: https://doi.org/10.1007/978-1-4684-9330-6_29
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-9332-0
Online ISBN: 978-1-4684-9330-6
eBook Packages: Springer Book Archive