Derivation of the Cartwright-Levinson theorem from the Kolmogorov theorem

Abstract

One says that an entire function f of finite exponential type belongs to the Cartwright class C, if Let N+(r)(N−(r)) denote the number of zeros of the function f in the disk ¦z¦⩾R, such that Re z⩾0 (Re z<0, respectively). We give a simple derivation of the folfollowing result of importance in the theory of entire functions, from a weak type Kolmogorov inequality.

Locations

• Journal of Soviet Mathematics - View - PDF