On subharmonic functions in the half-plane of
infinite order with radially distributed measure

K. G. Malyutin; T. I. Malyutina; I. I. Kozlova

If a proper subharmonic function of infinite order has the full measure at the finite system of rays in the upper half-plane, then its lower order also equals infinity.

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

2. J.B. Miles, Quotient representations of meromorphic functions, J. d0 Analyse Math., 25 (1972), 371–388.

3. A.A. Kondratyuk, The Fourier series method for entire and meromorphic functions of completely regular growth, Mat. Sb., 106(148) (1978), №3(7), 386–408; English transl. in Math. USSR-Sb., 35 (1979), №1, 63–84.

4. A.A. Kondratyuk, The Fourier series method for entire and meromorphic functions of completely regular growth. II, Mat. Sb., 113(155) (1980), №1(9), 118–132; English transl. in Math. USSR-Sb., 41 (1982), №1, 101–113.

5. A.A. Kondratyuk, The Fourier series method for entire and meromorphic functions of completely regular growth. III, Mat. Sb., 120(162) (1983), №3, 331–343; English transl. in Math. USSR-Sb., 48 (1984), №2, 327–338.

6. J.B. Miles, On entire functions of infinite order with radially distributed zeros, Pacif. J. Math., 81 (1979), №1, 131–157.

7. I.I. Kozlova, Subharmonic function of infinite order in the half-plane, Zbirnyk prats’ In-tu matematyky NAN Ukrainu, 9 (2012), №2, 207–213. (in Russian)

8. A.F.Grishin, Continuity and asymptotical continuity of subharmonic functions, Mathematical Physics, Analysis and Geometry, 1 (1994), №2, 193–215. (in Russian)

9. K.G. Malyutin, 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.

10. B.Ya. Levin, Distribution of zeros of entire functions. – English revised edition Amer. Math. Soc, Providence, RI, 1980.

	On subharmonic functions in the half-plane of infinite order with radially distributed measure
Author	K. G. Malyutin, T. I. Malyutina, I. I. Kozlova malyutinkg@yahoo.com State University of Sumy
Abstract	If a proper subharmonic function of infinite order has the full measure at the finite system of rays in the upper half-plane, then its lower order also equals infinity.
Keywords	proper subharmonic function; infinite order; lower order; Fourier coefficients; full measure
Reference	1. L.A. Rubel, B.A. Taylor, Fourier series method for meromorphic and entire functions, Bull. Soc. Math. France, 96 (1968), 53–96. 2. J.B. Miles, Quotient representations of meromorphic functions, J. d0 Analyse Math., 25 (1972), 371–388. 3. A.A. Kondratyuk, The Fourier series method for entire and meromorphic functions of completely regular growth, Mat. Sb., 106(148) (1978), №3(7), 386–408; English transl. in Math. USSR-Sb., 35 (1979), №1, 63–84. 4. A.A. Kondratyuk, The Fourier series method for entire and meromorphic functions of completely regular growth. II, Mat. Sb., 113(155) (1980), №1(9), 118–132; English transl. in Math. USSR-Sb., 41 (1982), №1, 101–113. 5. A.A. Kondratyuk, The Fourier series method for entire and meromorphic functions of completely regular growth. III, Mat. Sb., 120(162) (1983), №3, 331–343; English transl. in Math. USSR-Sb., 48 (1984), №2, 327–338. 6. J.B. Miles, On entire functions of infinite order with radially distributed zeros, Pacif. J. Math., 81 (1979), №1, 131–157. 7. I.I. Kozlova, Subharmonic function of infinite order in the half-plane, Zbirnyk prats’ In-tu matematyky NAN Ukrainu, 9 (2012), №2, 207–213. (in Russian) 8. A.F.Grishin, Continuity and asymptotical continuity of subharmonic functions, Mathematical Physics, Analysis and Geometry, 1 (1994), №2, 193–215. (in Russian) 9. K.G. Malyutin, 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. 10. B.Ya. Levin, Distribution of zeros of entire functions. – English revised edition Amer. Math. Soc, Providence, RI, 1980.
Pages	179-183
Volume	41
Issue	2
Year	2014
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

On subharmonic functions in the half-plane of infinite order with radially distributed measure