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On the growth of an algebroid function with radially distributed values

Nan Wu, Jian Hua Zheng (2015)

Annales Polonici Mathematici

We investigate how the growth of an algebroid function could be affected by the distribution of the arguments of its a-points in the complex plane. We give estimates of the growth order of an algebroid function with radially distributed values, which are counterparts of results for meromorphic functions with radially distributed values.

On the growth of solutions of some higher order linear differential equations

Abdallah El Farissi, Benharrat Belaidi (2012)

Applications of Mathematics

In this paper we discuss the growth of solutions of the higher order nonhomogeneous linear differential equation f ( k ) + A k - 1 f ( k - 1 ) + + A 2 f ' ' + ( D 1 ( z ) + A 1 ( z ) e a z ) f ' + ( D 0 ( z ) + A 0 ( z ) e b z ) f = F ( k 2 ) , where a , b are complex constants that satisfy a b ( a - b ) 0 and A j ( z ) ( j = 0 , 1 ...

On the growth of the resolvent operators for power bounded operators

Olavi Nevanlinna (1997)

Banach Center Publications

Outline. In this paper I discuss some quantitative aspects related to power bounded operators T and to the decay of T n ( T - 1 ) . For background I refer to two recent surveys J. Zemánek [1994], C. J. K. Batty [1994]. Here I try to complement these two surveys in two different directions. First, if the decay of T n ( T - 1 ) is as fast as O(1/n) then quite strong conclusions can be made. The situation can be thought of as a discrete version of analytic semigroups; I try to motivate this in Section 1 by demonstrating the...

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