Browsing by Subject "Functions, Entire."
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Item Open Access Distance between a maximum point and the zero set of an entire function(2006) Üreyen, Adem ErsinWe obtain asymptotical bounds from below for the distance between a maximum modulus point and the zero set of an entire function. Known bounds (Macintyre, 1938) are more precise, but they are valid only for some maximum modulus points. Our bounds are valid for all maximum modulus points and moreover, up to a constant factor, they are unimprovable. We consider entire functions of regular growth and obtain better bounds for these functions. We separately study the functions which have very slow growth. We show that the growth of these functions can not be very regular and obtain precise bounds for their growth irregularity. Our bounds are expressed in terms of some smooth majorants of the growth function. These majorants are defined by using orders, types, (strong) proximate orders of entire functions.Item Open Access On power series with one singular point at circumference of convergence(2002) Yardımcı, UmutWe obtain two refinements of Faber’s theorem related to power series with one singular point at circumference of convergence. The first one characterizes growth at the singular point in more precise scale of growth. The second one characterizes the growth at the singular point using series expansions both inside and outside the disc of convergence.