منابع مشابه
The Size of Wiman-valiron Disks
Wiman-Valiron theory and results of Macintyre about “flat regions” describe the asymptotic behavior of entire functions in certain disks around points of maximum modulus. We estimate the size of these disks for Macintyre’s theory from above and below.
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the Valiron deficiency of the value a for f(z). (We assume familiarity with the standard notations and basic results of meromorphic function theory, as described for instance in [2].) Some fifty years ago, Valiron [5, 6] constructed examples of integral functions f(z) of order 1 for which A (a , / ) = 1 for an uncountable set of fl-values. On the other hand, he also showed [4] that an integral ...
متن کاملSpectral theory in several variables
1. Recall the spectrum of a bounded linear operator T ∈ B(X) on a Banach space X, more generally a Banach algebra element a ∈ A: 1.1 σ(a) = σA(a) = {λ ∈ C : a− λ 6∈ A−1}, where of course 1.2 a ∈ A−1 ⇐⇒ ∃a′, a′′ ∈ A, a′a = 1 = aa′′ : for example for square matrices A = Cn×n we have the well worn cliche 1.3 σ(a) = σA(a) = {λ ∈ C : det(a− λ) = 0}; for continuous functions A = C(Ω) on compact Hausd...
متن کاملWiman and Arima Theorems for Quasiregular Mappings
It follows from the Ahlfors theorem that an entire holomorphic function f of order ρ has no more than 2ρ distinct asymptotic curves where r stands for the largest integer ≤ r. This theorem does not give any information if ρ < 1/2, This case is covered by two theorems: if an entire holomorphic function f has order ρ < 1/2 then lim supr→∞min|z| r |f z | ∞ Wiman 1 and if f is an entire holomorphic...
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Hölder estimates for spatial second derivatives are proved for solutions of fully nonlinear parabolic equations in two space variables. Related techniques extend the regularity theory for fully nonlinear parabolic equations in higher dimensions.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1995
ISSN: 0002-9947
DOI: 10.2307/2155043