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

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{MZM_2014_96_3_a10,
     author = {K. G. Malyutin and I. I. Kozlova and N. Sadik},
     title = {Canonical {Functions} of {Admissible} {Measures} in the {Half-Plane}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {418--431},
     publisher = {mathdoc},
     volume = {96},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_3_a10/}
}
TY  - JOUR
AU  - K. G. Malyutin
AU  - I. I. Kozlova
AU  - N. Sadik
TI  - Canonical Functions of Admissible Measures in the Half-Plane
JO  - Matematičeskie zametki
PY  - 2014
SP  - 418
EP  - 431
VL  - 96
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2014_96_3_a10/
LA  - ru
ID  - MZM_2014_96_3_a10
ER  - 
%0 Journal Article
%A K. G. Malyutin
%A I. I. Kozlova
%A N. Sadik
%T Canonical Functions of Admissible Measures in the Half-Plane
%J Matematičeskie zametki
%D 2014
%P 418-431
%V 96
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2014_96_3_a10/
%G ru
%F MZM_2014_96_3_a10
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/

[1] A. A. Goldberg, I. V. Ostrovskii, Raspredelenie znachenii meromorfnykh funktsii, Nauka, M., 1970 | MR | Zbl

[2] A. F. Grishin, “Nepreryvnost i asimptoticheskaya nepreryvnost subgarmonicheskikh funktsii. I”, Matematicheskaya fizika, analiz, geometriya, 1:2 (1994), 193–215 | MR | Zbl

[3] N. V. Govorov, Kraevaya zadacha Rimana s beskonechnym indeksom, Nauka, M., 1986 | MR | Zbl

[4] W. K. Hayman, “Questions of regularity connected with Phragmén–Lindelöf principle”, J. Math. Pures Appl. (9), 35 (1956) | MR | Zbl

[5] J.-I. Itô, “Subharmonic functions in the half-plane”, Trans. Am. Math. Soc., 129:3 (1967) | MR | Zbl

[6] L. A. Rubel, “A generalised canonical product”, Sovremennye problemy teorii analiticheskikh funktsii, Nauka, M., 1966, 264–270 | MR | Zbl

[7] B. N. Khabibullin, “Posledovatelnosti nulei golomorfnykh funktsii, predstavlenie meromorfnykh funktsii i garmonicheskie minoranty”, Matem. sb., 198:2 (2007), 121–160 | DOI | MR | Zbl

[8] B. N. Khabibullin, “Posledovatelnost nulei golomorfnykh funktsii, predstavlenie meromorfnykh funktsii. II. Tselye funktsii”, Matem. sb., 200:2 (2009), 129–158 | DOI | MR | Zbl

[9] K. G. Malyutin, V. A. Gerasimenko, “Obobschennye kanonicheskie proizvedeniya v kompleksnoi ploskosti”, Vest. Kharkovsk. un-ta. Ser. Matem., prikl. matem. i mekh., 790:57 (2007), 198–205 | Zbl

[10] K. G. Malyutin, N. M. Sadyk, “Predstavlenie subgarmonicheskikh funktsii v poluploskosti”, Matem. sb., 198:12 (2007), 47–62 | DOI | MR | Zbl

[11] G. Deng, Growth Estimates and Integral Representations of Harmonic and Subharmonic Functions, arXiv: math.FA/0906.1679v1

[12] K. G. Malyutin, “Ryady Fure i $\delta$-subgarmonicheskie funktsii konechnogo $\gamma$-tipa v poluploskosti”, Matem. sb., 192:6 (2001), 51–70 | DOI | MR | Zbl

[13] E. Titchmarsh, Teoriya funktsii, Nauka, M., 1980 | MR | Zbl

[14] B. Ya. Levin, Raspredelenie kornei tselykh funktsii, Gostekhizdat, M., 1956 | MR | Zbl

[15] R. Edvards, Ryady Fure v sovremennom izlozhenii, T. 1, Mir, M., 1985 | MR | Zbl

[16] U. Kheiman, P. Kennedi, Subgarmonicheskie funktsii, Mir, M., 1980 | MR | Zbl