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On an analytic approach to the Fatou conjecture

Genadi Levin (2002)

Fundamenta Mathematicae

Let f be a quadratic map (more generally, f ( z ) = z d + c , d > 1) of the complex plane. We give sufficient conditions for f to have no measurable invariant linefields on its Julia set. We also prove that if the series n 0 1 / ( f ) ' ( c ) converges absolutely, then its sum is non-zero. In the proof we use analytic tools, such as integral and transfer (Ruelle-type) operators and approximation theorems.

On an entire function represented by multiple Dirichlet series

Lakshika Chutani (2021)

Mathematica Bohemica

Consider the space L of entire functions represented by multiple Dirichlet series that becomes a non uniformly convex Banach space which is also proved to be dense, countable and separable. Continuing further, for the given space L the characterization of bounded linear transformations in terms of matrix and characterization of linear functional has been obtained.

On Bloch functions and gap series.

Daniel Girela (1991)

Publicacions Matemàtiques

Kennedy obtained sharp estimates of the growth of the Nevanlinna characteristic of the derivative of a function f analytic and with bounded characteristic in the unit disc. Actually, Kennedy's results are sharp even for VMOA functions. It is well known that any BMOA function is a Bloch function and any VMOA function belongs to the little Bloch space. In this paper we study the possibility of extending Kennedy's results to certain classes of Bloch functions. Also, we prove some more general results...

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