Subharmonic function of infinite order in the half-plane

Abstract

Let 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
• fullmeasure.

References

1. Miles, J.B., On entire functions of innite order with radially distributed zeros, Pacif. J. Math. Derg. 81(1) (1979), 131–157.
2. Grishin, A.F., Continuity and asymptotic continuity of subharmonic functions, Mat. Fiz., Anal., Geom. Derg. 1 (1994), 193–215 (in Russian).
3. Malyutin, K.G., Fourier series and -subharmonic functions of nite-type in a half-plane, Mat. Sb. Derg. 192(6) (2001), 51–70 (in Russian); English transl. in Sb.: Math. 192(6) (2001).
4. Levin, B.Ya., Distribution of Zeros of Entire Functions, English revised edition Amer. Math. Soc, Providence, RI, 523pp. MR 81k:30011.