Fourier series and delta-subharmonic functions of zero-type in a half-plane

K.G.Malyutin; T.I.Malyutina

In terms of Fourier coefficients and associated complete measures a class of just $\delta$-subharmonic functions in a half-plane of a zero type is described.

1. Rubel L.A. and Taylor B.A. Fourier series method for meromorphic and entire functions, Bull. Soc. Math. France. 96(1968), 53--96.

2. Miles J.B. Quotient representations of meromorphic functions, J. Anal. Math. (1972), 371--388.

3. Kondratyuk A.A. The Fourier series method for entire and meromorphic functions of completely regular growth. I, Mat. Sb. 106(148) (1978), 386--408; English transl. in Math. USSR-Sb. 35 (1979).

4. Kondratyuk A.A. The Fourier series method for entire and meromorphic functions of completely regular growth. II, Mat. Sb. 113(155) (1980), 118--132; English transl. in Math. USSR-Sb. 41 (1982).

5. Kondratyuk A.A. The Fourier series method for entire and meromorphic functions of completely regular growth. III, Mat. Sb. 120(162) (1983), 331--343; English transl. in Math. USSR-Sb. 48 (1984).

6. Malyutin K.G. Fourier series and $\delta$-subharmonic functions of finite $\gamma$-type in a half-plane, Mat. Sb. 192 (2001), № 6, 51--70; English transl. in Sb.: Math. 192 (2001), № 6.

7. Grishin A.F. Continuity and asymptotic continuity of subharmonic functions, Mat. Fiz., Anal., Geom. 1 (1994), 193--215. (Russian)

8. Fedorov M.A. and Grishin A.F. Some questions of the Nevanlinna theory for the complex half-plane, Math. Phys., Anal., Geom. 1 (1998), № 3, 223--271.

9. Ahiezer N.I. Elements of the theory of elliptic functions. Nauka, Moskow 1970; English transl., Amer. Math. Soc., Providence, RI, 1990.

10. Malyutin K.G. Fourier series and $\delta$-subharmonic functions, Trudy Inst. Problem Mat. Mekh. Akad. Nauk Ukr. SSR 3 (1988), 146--157. (Russian)

11. Govorov N.V. Riemann's boundary problem with infinite index. Nauka, Moscow 1986; English transl., Birkhäuser, Basel, 1994.

	Fourier series and delta-subharmonic functions of zero-type in a half-plane
Author	K.G.Malyutin, T.I.Malyutina malyutinkg@yahoo.com Agrarian University of Sumy, Ukrainian Academy of Banking
Abstract	In terms of Fourier coefficients and associated complete measures a class of just $\delta$-subharmonic functions in a half-plane of a zero type is described.
Keywords	Fourier coefficient, associated complete measure, subharmonic function, zero type
DOI	doi:10.30970/ms.30.2.132-138
Reference	1. Rubel L.A. and Taylor B.A. Fourier series method for meromorphic and entire functions, Bull. Soc. Math. France. 96(1968), 53--96. 2. Miles J.B. Quotient representations of meromorphic functions, J. Anal. Math. (1972), 371--388. 3. Kondratyuk A.A. The Fourier series method for entire and meromorphic functions of completely regular growth. I, Mat. Sb. 106(148) (1978), 386--408; English transl. in Math. USSR-Sb. 35 (1979). 4. Kondratyuk A.A. The Fourier series method for entire and meromorphic functions of completely regular growth. II, Mat. Sb. 113(155) (1980), 118--132; English transl. in Math. USSR-Sb. 41 (1982). 5. Kondratyuk A.A. The Fourier series method for entire and meromorphic functions of completely regular growth. III, Mat. Sb. 120(162) (1983), 331--343; English transl. in Math. USSR-Sb. 48 (1984). 6. Malyutin K.G. Fourier series and $\delta$-subharmonic functions of finite $\gamma$-type in a half-plane, Mat. Sb. 192 (2001), № 6, 51--70; English transl. in Sb.: Math. 192 (2001), № 6. 7. Grishin A.F. Continuity and asymptotic continuity of subharmonic functions, Mat. Fiz., Anal., Geom. 1 (1994), 193--215. (Russian) 8. Fedorov M.A. and Grishin A.F. Some questions of the Nevanlinna theory for the complex half-plane, Math. Phys., Anal., Geom. 1 (1998), № 3, 223--271. 9. Ahiezer N.I. Elements of the theory of elliptic functions. Nauka, Moskow 1970; English transl., Amer. Math. Soc., Providence, RI, 1990. 10. Malyutin K.G. Fourier series and $\delta$-subharmonic functions, Trudy Inst. Problem Mat. Mekh. Akad. Nauk Ukr. SSR 3 (1988), 146--157. (Russian) 11. Govorov N.V. Riemann's boundary problem with infinite index. Nauka, Moscow 1986; English transl., Birkhäuser, Basel, 1994.
Pages	132-138
Volume	30
Issue	2
Year	2008
Journal	Matematychni Studii
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