Approximation by Bounded Analytic Functions: Uniform Convergence as Implied by Mean Convergence

2000 ◽  
pp. 442-449
Author(s):  
J. L. Walsh
Keyword(s):  
Uniform Convergence ◽  
Analytic Functions ◽  
Bounded Analytic Functions ◽  
Mean Convergence

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 Bohr–Rogosinski Inequalities for Bounded Analytic Functions

2020 ◽  
Vol 41 (11) ◽  
pp. 2110-2119
Author(s):  
Seraj A. Alkhaleefah ◽  
Ilgiz R. Kayumov ◽  
Saminathan Ponnusamy
Keyword(s):  
Analytic Functions ◽  
Bounded Analytic Functions

scholarly journals The arc-length variation of analytic capacity and a conformal geometry

1992 ◽  
Vol 125 ◽  
pp. 151-216
Author(s):  
Takafumi Murai
Keyword(s):  
Banach Space ◽  
Complex Plane ◽  
Analytic Functions ◽  
Conformal Geometry ◽  
Supremum Norm ◽  
Length Variation ◽  
Analytic Capacity ◽  
Arc Length ◽  
Bounded Analytic Functions ◽  
Extended Complex

For a domain Ω in the extended complex plane C ∪{∞}, H∞(Ω) denotes the Banach space of bounded analytic functions in Ω with supremum norm ∥ · ∥H∞ For ζ ∈ Ω, we putwhere f′(∞) = lim,z→∞z{f (∞) = f(z)} if ζ = ∞.

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