2017
Том 69
№ 5

All Issues

Extension and approximation of functions subharmonic in a half plane. Impossibility of extension of plurisubharmonic functions

Rashkovskii A. Yu., Ronkin L. I.

Full text (.pdf)


Abstract

We construct different extensions of functions subharmonic in a half plane to the whole plane. The results obtained are applied to the approximation of subharmonic functions of finite order in a half plane by the logarithm of the modulus of an entire function. It is shown that the problem of extension of a plurisubharmonic function may have no solution.

English version (Springer): Ukrainian Mathematical Journal 46 (1994), no. 8, pp 1117-1130.

Citation Example: Rashkovskii A. Yu., Ronkin L. I. Extension and approximation of functions subharmonic in a half plane. Impossibility of extension of plurisubharmonic functions // Ukr. Mat. Zh. - 1994. - 46, № 8. - pp. 1017–1030.

Full text