The order of normality and meromorphic univalent functions
The Paley-Wiener-Levinson theorem revisited.
The range of a random function defined in the unit disk
The Schwarz-Pick theorem and its applications
Various derivative estimates for functions of exponential type in a half-plane are proved in this paper. The reader will also find a related result about functions analytic in a quadrant. In addition, the paper contains a result about functions analytic in a strip. Our main tool in this study is the Schwarz-Pick theorem from the geometric theory of functions. We also use the Phragmén-Lindelöf principle, which is of course standard in such situations.
The second coefficient of a function with all derivatives univalent.
The second main theorem for algebroid functions.
The set of Lindelöf points for meromorphic functions
The sharpness of some cluster set results.
The singular directions of solutions of some equations.
The spectrum of Schrödinger operators with random magnetic fields
We shall consider the Schrödinger operators on with the magnetic field given by a nonnegative constant field plus random magnetic fields of the Anderson type or of the Poisson-Anderson type. We shall investigate the spectrum of these operators by the method of the admissible potentials by Kirsch-Martinelli. Moreover, we shall prove the lower Landau levels are infinitely degenerated eigenvalues when the constant field is sufficiently large, by estimating the growth order of the eigenfunctions...
The spherical derivative of meromorphic functions.
The structure of disjoint iteration groups on the circle
The aim of the paper is to investigate the structure of disjoint iteration groups on the unit circle , that is, families of homeomorphisms such that and each either is the identity mapping or has no fixed point ( is an arbitrary -divisible nontrivial (i.e., ) abelian group).
The Taylor series and growth of means.
The value-distribution of lacunary series and a conjecture of Paley
The purpose of this paper is to establish a theorem which answers a conjecture of Paley on the distribution of values of Hadamard lacunary series and which is useful to study the Peano curve property of such series.
The Winding of an Analytic Function.
The zero distribution and uniqueness of difference-differential polynomials
We consider the zero distribution of difference-differential polynomials of meromorphic functions and present some results which can be seen as the discrete analogues of the Hayman conjecture. In addition, we also investigate the uniqueness of difference-differential polynomials of entire functions sharing one common value. Our theorems improve some results of Luo and Lin [J. Math. Anal. Appl. 377 (2011), 441-449] and Liu, Liu and Cao [Appl. Math. J. Chinese Univ. 27 (2012), 94-104].
Transcendance et indépendance algébrique des valeurs de fonctions méromorphes
Transcendency of Local Conjugacies in Complex Dynamics and Transcendency of their Values.
Travaux récents de G. V. Čudnovskij
Two sufficient conditions for the MacLane class A