Abstract
The origin of the Bloch Principle can seemingly be traced back to Bloch’s dictum, “Nihil est in infinito quod non prius fuerit in finito” found on p. 2 of his 1926 monograph, as well as on p. 84 of [1926b]. It may be translated as: Nothing exists in the infinite plane that has not been previously done in the finite disk. In modern parlance it is the hypothesis that a family of analytic (meromorphic) functions which have a common property р in a domain Ω will in general be a normal family if р reduces an analytic (meromorphic) function in to a constant. The property of omitting two (resp. three) given values of the FNT is one such example. However, the connection between the modern Bloch Principle and Bloch’s original utterance is tenuous at best.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media New York
About this chapter
Cite this chapter
Schiff, J.L. (1993). Bloch Principle. In: Normal Families. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0907-2_4
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0907-2_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97967-0
Online ISBN: 978-1-4612-0907-2
eBook Packages: Springer Book Archive