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The angular value distribution of analytic and random analytic
functions (in Ukrainian) |
| Author |
M. P. Mahola, P. V. Filevych
marichka_stanko@ukr.net, filevych@mail.ru
Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України,
Прикарпатський національний університет ім. В. Стефаника
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| Abstract |
Let a∈C, f(z)=∑cnzn be an analytic function in the disk |z|<1 such that Sf(r):=(∑|cn|2r2n)12→+∞, r→1, Nf(r,α,β,a) be the integrated counting function of a-points of f in the sector 0<|z|≤r, α≤argαz<β, Nf(r,a)=Nf(r,0,2π,a), and E⊂(0,1) be a set such that sup. It is proved that if N_{f}(r,a)\sim\ln S_{f}(r), E\ni r\to1, then N_{f}(r,\alpha,\beta,a)\sim\frac{\beta-\alpha}{2\pi}\ln S_{f}(r), E\ni r\to1, uniformly in \alpha<\beta\le\alpha+2\pi. |
| Keywords |
value distribution, analytic function; random analytic function; integrated counting function; angular integrated counting function |
| Reference |
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| Pages |
147-153 |
| Volume |
38 |
| Issue |
2 |
| Year |
2012 |
| Journal |
Matematychni Studii |
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