Fourier series and {delta}subharmonic functions of finite {gamma}type in a halfplane
Abstract
Let {gamma}(r) be a growth function and let v(z) be a proper {delta}subharmonic function in the sense of Grishin in a complex halfplane, that is v=v{sub 1}v{sub 2}, where v{sub 1} and v{sub 2} are proper subharmonic functions (limsup{sub z{yields}}{sub t}v{sub i}(z){<=}0, for each real t, i=1,2), let {lambda}={lambda}{sub +}{lambda}{sub } be the full measure corresponding to v and let T(r,v) be its Nevanlinna characteristic. The class J{delta}({gamma}) of functions of finite {gamma}type is defined as follows: v element of J{delta}({gamma}) if T(r,v){<=}A{gamma}(Br)/r for some positive constants A and B. The Fourier coefficients of v are defined in the standard way. The central result of the paper is the equivalence of the following properties: (1) v element of J{delta}({gamma}); (2) N(r){<=}A{sub 1}{gamma}(B{sub 1}r)/r, where N(r)=N(r,{lambda}{sub +}) or N(r)=N(r,{lambda}{sub }), and c{sub k}(r,v){<=}A{sub 2}{gamma}(B{sub 2}r). It is proved in addition that J{delta}({gamma})=JS({gamma})JS({gamma}), where JS({gamma}) is the class of proper subharmonic functions of finite {gamma}type.
 Authors:
 Ukrainian Academy of Banking, Sumy (Ukraine)
 Publication Date:
 OSTI Identifier:
 21205612
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Sbornik. Mathematics; Journal Volume: 192; Journal Issue: 6; Other Information: DOI: 10.1070/SM2001v192n06ABEH000572; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPLEX MANIFOLDS; FUNCTIONS; MATHEMATICAL LOGIC
Citation Formats
Malyutin, K G. Fourier series and {delta}subharmonic functions of finite {gamma}type in a halfplane. United States: N. p., 2001.
Web. doi:10.1070/SM2001V192N06ABEH000572; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Malyutin, K G. Fourier series and {delta}subharmonic functions of finite {gamma}type in a halfplane. United States. doi:10.1070/SM2001V192N06ABEH000572; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Malyutin, K G. Sat .
"Fourier series and {delta}subharmonic functions of finite {gamma}type in a halfplane". United States.
doi:10.1070/SM2001V192N06ABEH000572; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
@article{osti_21205612,
title = {Fourier series and {delta}subharmonic functions of finite {gamma}type in a halfplane},
author = {Malyutin, K G},
abstractNote = {Let {gamma}(r) be a growth function and let v(z) be a proper {delta}subharmonic function in the sense of Grishin in a complex halfplane, that is v=v{sub 1}v{sub 2}, where v{sub 1} and v{sub 2} are proper subharmonic functions (limsup{sub z{yields}}{sub t}v{sub i}(z){<=}0, for each real t, i=1,2), let {lambda}={lambda}{sub +}{lambda}{sub } be the full measure corresponding to v and let T(r,v) be its Nevanlinna characteristic. The class J{delta}({gamma}) of functions of finite {gamma}type is defined as follows: v element of J{delta}({gamma}) if T(r,v){<=}A{gamma}(Br)/r for some positive constants A and B. The Fourier coefficients of v are defined in the standard way. The central result of the paper is the equivalence of the following properties: (1) v element of J{delta}({gamma}); (2) N(r){<=}A{sub 1}{gamma}(B{sub 1}r)/r, where N(r)=N(r,{lambda}{sub +}) or N(r)=N(r,{lambda}{sub }), and c{sub k}(r,v){<=}A{sub 2}{gamma}(B{sub 2}r). It is proved in addition that J{delta}({gamma})=JS({gamma})JS({gamma}), where JS({gamma}) is the class of proper subharmonic functions of finite {gamma}type.},
doi = {10.1070/SM2001V192N06ABEH000572; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},
journal = {Sbornik. Mathematics},
number = 6,
volume = 192,
place = {United States},
year = {Sat Jun 30 00:00:00 EDT 2001},
month = {Sat Jun 30 00:00:00 EDT 2001}
}

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