Applications to Entire Functions

Part of the Birkhäuser Advanced Texts / Basler Lehrbücher book series (BAT)


Let f(z) be an entire function. The function u(z) ≔ log|f(z)| is subharmonic in ℝ2(= ℂ). Hence the scale of growth subharmonic functions considered in Section 2.8 is transferred completely to entire functions. We will mark passing to entire function by changing index u for index f. For example,
$$ M\left( {r,f} \right): = M\left( {r,log\left| f \right|} \right),T\left( {r,f} \right): = T\left( {r,log\left| f \right|} \right). $$
If u(z) ≔ log|f(z)| has order ρ[u] = ρ, then f(z) has order ρ[f] ≔ ρ and so on.


Maximum Principle Unit Circle Entire Function Meromorphic Function Subharmonic Function 
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© Birkhäuser Verlag AG 2009

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