Inverse formulae for Fourier coefficients of delta-subharmonic functions in a~half-plane

K.G.Malyutin

Applying the Fourier series method we obtain inverse relations for the Fourier coefficients of delta-subharmonic function in the upper complex half-plane. These inverse relations as well as direct ones can be considered as generalizations of well-known Carleman's formula.

1. ~Rubel L.A. A Fourier series method for entire functions, Duke Math. J. 30(1963), 437-442.

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

3. ~Miles J.B. Quotient representations of meromorphic functions, J. ${\rm d'}$ Analyse Math. 25(1972), 371-388.

4. ~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).

5. ~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).

6. ~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).

7. ~Malyutin K.G. Fourier series and $\delta$-subharmonic functions of finite $\gamma$-type in a half-plane, Mat. Sb. 192(6) (2001), 51-70; English transl. in Sb.: Math. 192(6) (2001).

8. ~Malyutin K.G., Nazim Sadik. Delta-subharmonic functions of completely regular growth in the half-plane, Russian Acad. Sci. Docl. Math. 380(3) (2001), 1-3.

9. ~Malyutin K.G., Nazim Sadik. Presentation of subharmonic functions in a half-plane, Mat. Sb. 198(12) (2007), 47-62; English transl. in Sb.: Math. 198(12) (2007).

10. ~Malyutin K.G., Malyutina T.I. Fourier series and delta-subharmonic functions of zero-type in a half-plane, Matematychni Studii. 30(2) (2008), 133 - 138.

11. ~Grishin A.F. Continuity and asymptotical continuity of subharmonic functions, Mathematical Physics, Analysis and Geometry. 1(2) (1994), 193-215.

12. ~Fedorov M.A., A.F. Grishin A.F. Some Questions of the Nevanlinna Theory for the Complex Half-Plane, Mathematical Physics, Analysis and Geometry. 1(3) (1998), 223-271.

13. ~Malyutin K.G. Fourier series and delta-subharmonic functions, Proceedings of IPMM NAN Ukraine. 3 (1998), 146-157.

14. ~Rubel L.A. Entire and meromorphic functions. Springer, New York, Berlin, Heidelberg 1995.

15. ~~Kondratyuk A.A. The Fourier series and meromorphic functions. "Vyshcha shkola", Lviv 1988.

	Inverse formulae for Fourier coefficients of delta-subharmonic functions in a~half-plane
Author	K.G.Malyutin malyutinkg@yahoo.com State University of Sumy,
Abstract	Applying the Fourier series method we obtain inverse relations for the Fourier coefficients of delta-subharmonic function in the upper complex half-plane. These inverse relations as well as direct ones can be considered as generalizations of well-known Carleman's formula.
Keywords	inverse forlmula, Fourier coefficient, delta-subharmonic function, half-plane
DOI	doi:10.30970/ms.32.2.210-215
Reference	1. ~Rubel L.A. A Fourier series method for entire functions, Duke Math. J. 30(1963), 437-442. 2. ~Rubel L.A., Taylor B.A. Fourier series method for meromorphic and entire functions, Bull. Soc. Math. France. 96(1968), 53-96. 3. ~Miles J.B. Quotient representations of meromorphic functions, J. ${\rm d'}$ Analyse Math. 25(1972), 371-388. 4. ~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). 5. ~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). 6. ~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). 7. ~Malyutin K.G. Fourier series and $\delta$-subharmonic functions of finite $\gamma$-type in a half-plane, Mat. Sb. 192(6) (2001), 51-70; English transl. in Sb.: Math. 192(6) (2001). 8. ~Malyutin K.G., Nazim Sadik. Delta-subharmonic functions of completely regular growth in the half-plane, Russian Acad. Sci. Docl. Math. 380(3) (2001), 1-3. 9. ~Malyutin K.G., Nazim Sadik. Presentation of subharmonic functions in a half-plane, Mat. Sb. 198(12) (2007), 47-62; English transl. in Sb.: Math. 198(12) (2007). 10. ~Malyutin K.G., Malyutina T.I. Fourier series and delta-subharmonic functions of zero-type in a half-plane, Matematychni Studii. 30(2) (2008), 133 - 138. 11. ~Grishin A.F. Continuity and asymptotical continuity of subharmonic functions, Mathematical Physics, Analysis and Geometry. 1(2) (1994), 193-215. 12. ~Fedorov M.A., A.F. Grishin A.F. Some Questions of the Nevanlinna Theory for the Complex Half-Plane, Mathematical Physics, Analysis and Geometry. 1(3) (1998), 223-271. 13. ~Malyutin K.G. Fourier series and delta-subharmonic functions, Proceedings of IPMM NAN Ukraine. 3 (1998), 146-157. 14. ~Rubel L.A. Entire and meromorphic functions. Springer, New York, Berlin, Heidelberg 1995. 15. ~~Kondratyuk A.A. The Fourier series and meromorphic functions. "Vyshcha shkola", Lviv 1988.
Pages	210-215
Volume	32
Issue	2
Year	2009
Journal	Matematychni Studii
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