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Mat. Zametki, 2014, Volume 96, Issue 3, Pages 418–431 (Mi mz9685)  

Canonical Functions of Admissible Measures in the Half-Plane

K. G. Malyutina, I. I. Kozlovaa, N. Sadikb

a Sumy State University
b İstanbul University, Turkey

Abstract: For a $\gamma$-admissible measure $\lambda$ in the upper half-plane, we introduce the notion of canonical function, generalizing the canonical Nevanlinna product for analytic functions of finite order in the half-plane. It is shown that, for any growth function $\gamma$ defined by the Boutroux proximate order, the given definition and the canonical Nevanlinna product coincide.

Keywords: $\gamma$-admissible measure, $\gamma$-weighted measure, canonical Nevanlinna product, subharmonic function, growth function, Boutroux proximate order, Valiron proximate order, Fourier coefficients of a measure.

DOI: https://doi.org/10.4213/mzm9685

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English version:
Mathematical Notes, 2014, 96:3, 391–402

Bibliographic databases:

UDC: 517.574
Received: 29.03.2012
Revised: 22.10.2013

Citation: K. G. Malyutin, I. I. Kozlova, N. Sadik, “Canonical Functions of Admissible Measures in the Half-Plane”, Mat. Zametki, 96:3 (2014), 418–431; Math. Notes, 96:3 (2014), 391–402

Citation in format AMSBIB
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