# Subharmonic functions of finite $(\gamma,\varepsilon)$-type in a half-plane

Author K. G. Malyutin, I. I. Kozlova
malyutinkg@yahoo.com
State University of Sumy

Abstract We obtain criterions for delta-subharmonic function to belong to the class of functions of finite $(\gamma,\varepsilon)$)-type in a half-plane. These criterions are formulated in terms of Fourier coefficients of a function.
Keywords proper subharmonic function; function of growth; Fourier coefficients; complete 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. d'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), ¹3(7), 386–408; English transl. in Math. USSR-Sb., 35 (1979), ¹1, 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), ¹1(9), 118–132; English transl. in Math. USSR-Sb., 41 (1982), ¹1, 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), ¹3, 331–343; English transl. in Math. USSR-Sb., 48(1984), ¹3, 327–338.

6. P. Noverraz, Fonctions plurisousharmoniques et analtiques dans les espaces vectoriels topologiques complexes, Ann. Inst. Fourier, 19 (1969), ¹2, 419–493.

7. K.G. Malyutin, Fourier series and $\delta$-subharmonic functions, Trudy Inst. Problem Mat. Mekh. Akad. Nauk Ukr., 3 (1998), 146–157. (in Russian)

8. K.G. Malyutin, Fourier series and $\delta$-subharmonic functions of finite $\gamma$-type in a half-plane, Mat. Sb., 192 (2001), ¹6, 51–70; English transl. in Sb. Math., 192 (2001), ¹6, 843–861.

9. B.N. Khabibullin, Growth of entire functions with given zeros and representation of meromorphic functions, Mathematical Notes, 73 (2003), ¹1–2, 110–124. (in Russian)

10. Yu.S. Protsyk, Subharmonic functions of finite $(\gamma,\varepsilon)$-type, Mat. Stud., 24 (2005), ¹1, 39–56.

11. A.F. Grishin, Continuity and asymptotical continuity of subharmonic functions, Mathematical Physics, Analysis and Geometry, 1 (1994), ¹2, 193–215. (in Russian)

12. N.I. Ahiezer, Elements of the theory of elleptic functions, Nauka, Moscow, 1970; English transl., Amer. Math. Soc., Providence, RI, 1990.

Pages 154-161
Volume 38
Issue 2
Year 2012
Journal Matematychni Studii
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