On special classes of entire functions whose zeros and growth are restricted

Abstract

The present paper is an investigation of the uniform limits on bounded sets of entire functions of genus ⩽ 2 p \leqslant \,2p whose zeros are real, or lie in an even number of sectors (or correspondingly on rays) of a certain size, both the number and size depending on p. A characterization of the uniform limits of entire functions of genus ⩽ 2 p \leqslant \,2p whose zeros lie in these sectors is given.