## Growth Theory of Subharmonic FunctionsIn this book an account of the growth theory of subharmonic functions is given, which is directed towards its applications to entire functions of one and several complex variables. The presentation aims at converting the noble art of constructing an entire function with prescribed asymptotic behaviour to a handicraft. For this one should only construct the limit set that describes the asymptotic behaviour of the entire function. All necessary material is developed within the book, hence it will be most useful as a reference book for the construction of entire functions. |

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arbitrarily small asymptotic canonical potential Carleson measure chain recurrent Check choose compact set completely regular growth consider continuous function contradicts convex function Corollary countable set CRG-function deﬁned deﬁnition denote dynamical system enclosed in G entire function equality example Exercise extremely overcomplete following assertion following holds following properties following theorem function f G A(p(r G SH(D G SH(p(r G U[p harmonic function harmonic polynomial Hence ideally complementing II(x implies inequality infinitely differentiable integral interval invariant Laplace operator Lemma Let us prove Let v G liminf limsup mass distribution maximum principle measure mesc minimal monotonically neighborhood non-integer nonempty obtain open set polynomial precompact Proof of Theorem Proposition prove Theorem proximate order pseudo-trajectory pt[u respect satisﬁes satisfies the condition Section squarable subharmonic function subset summand supp Suppose theorem Theorem trigonometric uniformly upper semicontinuous