Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-23T09:16:48.653Z Has data issue: false hasContentIssue false
  • English
  • Français

A local form of the Phragmén-lindelöf indicator

Published online by Cambridge University Press:  26 February 2010

Albert Edrei
Albert Edrei
Affiliation:
Syracuse University, Syracuse, New York
Get access

Extract

Let f(z) be an entire function. The definition of a Phragmén–Lindelöf indicator of f(z) requires the preliminary construction of a fairly regular comparison function V(r).

If f(z) is of order λ (0 < λ < + ∞), and of mean type, one takes

and associates with f(z) the indicator

Type
Research Article
Information
Mathematika , Volume 17 , Issue 1 , June 1970 , pp. 149 - 172
Copyright
Copyright © University College London 1970

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Cartwright, M. L., Integral functions (Cambridge, 1956).Google Scholar
2.Edrei, A., “The deficiencies of meromorphic functions of finite lower order”, Duke Math. J., 31 (1964), 1–22.CrossRefGoogle Scholar
3.Edrei, A., “Sums of deficiencies of meromorphic functions”, J. d'Analyse Math., 14 (1965), 79–107.CrossRefGoogle Scholar
4.Edrei, A., “Sums of deficiencies of meromorphic functions II”, J. d'Analyse Math., 19 (1967), 53–74.CrossRefGoogle Scholar
5.Edrei, A., “Locally tauberian theorems for meromorphic functions of lower order less than one”, Trans. Amer. Math. Soc., 140 (1969), 309–332.CrossRefGoogle Scholar
6.Edrei, A. and Fuchs, W. H. J., “Tauberian theorems for a class of meromorphic functions with negative zeros and positive poles”, Proc. Internat. Conf. Function Theory, Erevan, 1965 Nauka, Moscow, 1966), 339–358.Google Scholar
7.Gol'dberg, A. A., “On defects of meromorphic functions”, Dokl. Akad. Nauk SSSR, 98 (1954), 893–895.Google Scholar
8.Kjellberg, B., “On the minimum modulus of entire functions of lower order less than one”, Math. Scand., 8 (1960), 189–197.CrossRefGoogle Scholar
9.Nevanlinna, R., Eindeutige Analytische Funktionen, second edition (Berlin, 1953).CrossRefGoogle Scholar
10.Ostrovskii, I. V., “Deficiencies of meromorphic functions of order less than one”, Dokl. Akad. Nauk SSSR, 150 (1963), 32–35.Google Scholar
11.TeichmÜller, O., “Vermutungen und Satze tiber die Wertverteilung gebrochener Funktionen endlicher Ordnung”, Deutsche Mathematik, 4 (1939), 163–190.Google Scholar
12.Titchmarsh, E. C., The theory of functions, second edition (Oxford, 1950).Google Scholar
13.Valiron, G., “Directions de Borel des fonctions meromorphes”, Memorial des Sciences Math., 89 (1938).Google Scholar