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The range of a continuous linear functional over a class of functions defined by subordination

Published online by Cambridge University Press:  18 May 2009

Richard Fournier
Richard Fournier
Affiliation:
Département de Mathématiques et de StatistiqueUniversité de MontréalMontréal, QuebecCanadaH3C 3J7
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Let Δ = {z ∈ ℂ ⃒ ⃓z⃓ <1) and H(Δ) the set of analytic functions on Δ. We recall the definition of subordination between two functions, say ƒ and g, analytic on Δ: this means that f(0)= g(0) and there is a function ρ ∈ H (Δ) such that ρ(0) = 0, ⃒ ρ(z)⃒<1 if z ∈ Δ, and f(z) ≡ g(ρ(z)). Subordination between f and g will be denoted by

f<g. The Hadamard product (or convolution) of two functions and in H(Δ)is the function f * g ∈ H(Δ)definedas f * g (z)= .

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 3 , September 1990 , pp. 381 - 387
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

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