Geodesic
Canonical Functions of Admissible Measures in the Half-Plane
Matematičeskie zametki, Tome 96 (2014) no. 3, pp. 418-431

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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, Valiron proximate order, Fourier coefficients of a measure.
Mots-clés : Boutroux proximate order 
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     title = {Canonical {Functions} of {Admissible} {Measures} in the {Half-Plane}},
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K. G. Malyutin; I. I. Kozlova; N. Sadik. Canonical Functions of Admissible Measures in the Half-Plane. Matematičeskie zametki, Tome 96 (2014) no. 3, pp. 418-431. http://geodesic.mathdoc.fr/item/MZM_2014_96_3_a10/