Extremal Problems in the Theory of Bounded Analytic Functions

1951 ◽  
Vol 73 (1) ◽  
pp. 78 ◽  
Author(s):  
Zeev Nehari
Keyword(s):  
Analytic Functions ◽  
Extremal Problems ◽  
Bounded Analytic Functions

Local extremal problems for bounded analytic functions without zeros

2006 ◽  
Vol 70 (4) ◽  
pp. 841-856
Author(s):  
D V Prokhorov ◽  
S V Romanova
Keyword(s):  
Analytic Functions ◽  
Extremal Problems ◽  
Bounded Analytic Functions

scholarly journals On approximation by bounded analytic functions

1954 ◽  
Vol 5 (1-3) ◽  
pp. 191-196
Author(s):  
J. L. Walsh ◽  
J. P. Evans
Keyword(s):  
Analytic Functions ◽  
Bounded Analytic Functions

scholarly journals On the derivatives of bounded analytic functions

1964 ◽  
Vol 5 (3-4) ◽  
pp. 287-300 ◽  
Author(s):  
»ke Samuelsson
Keyword(s):  
Analytic Functions ◽  
Bounded Analytic Functions ◽  
Derivatives Of

scholarly journals Extremal Problems for Functions Starlike in the Exterior of the Unit Circle

1962 ◽  
Vol 14 ◽  
pp. 540-551 ◽  
Author(s):  
W. C. Royster
Keyword(s):  
Unit Circle ◽  
Analytic Functions ◽  
Upper Bounds ◽  
Extremal Problems ◽  
Simple Pole ◽  
Image Position ◽  
Inverse Functions ◽  
Variational Formulas

Let Σ represent the class of analytic functions(1)which are regular, except for a simple pole at infinity, and univalent in |z| > 1 and map |z| > 1 onto a domain whose complement is starlike with respect to the origin. Further let Σ- 1 be the class of inverse functions of Σ which at w = ∞ have the expansion(2).In this paper we develop variational formulas for functions of the classes Σ and Σ- 1 and obtain certain properties of functions that extremalize some rather general functionals pertaining to these classes. In particular, we obtain precise upper bounds for |b2| and |b3|. Precise upper bounds for |b1|, |b2| and |b3| are given by Springer (8) for the general univalent case, provided b0 =0.

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