Subharmonic function of infinite order in the half-plane

Yıl 2013, Cilt: 4 , 9 - 14, 19.03.2014

İrina Kozlova

Öz

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.

Anahtar Kelimeler

Proper subharmonic function , infinite order , lower order , Fourier coefficients , fullmeasure.

Kaynakça

• Miles, J.B., On entire functions of innite order with radially distributed zeros, Pacif. J. Math. Derg. 81(1) (1979), 131–157.
• Grishin, A.F., Continuity and asymptotic continuity of subharmonic functions, Mat. Fiz., Anal., Geom. Derg. 1 (1994), 193–215 (in Russian).
• 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).
• Levin, B.Ya., Distribution of Zeros of Entire Functions, English revised edition Amer. Math. Soc, Providence, RI, 523pp. MR 81k:30011.