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The hyper-order of solutions of certain linear complex differential equations

Guowei Zhang, Ang Chen (2010)

Annales Polonici Mathematici

We prove some theorems on the hyper-order of solutions of the equation f ( k ) - e Q f = a ( 1 - e Q ) , where Q is an entire function, which is a polynomial or not, and a is an entire function whose order can be larger than 1. We improve some results by J. Wang and X. M. Li.

The Laguerre inequality and the distribution of zeros of entire functions

George Csordas, Alain Escassut (2005)

Annales mathématiques Blaise Pascal

The Laguerre inequality and the distribution of zeros of real entire functions are investigated with the aid of certain infinite-order differential operators. The paper includes new proofs, problems, conjectures and many illustrative examples and counterexamples.

The Schwarz-Pick theorem and its applications

M. Qazi, Q. Rahman (2011)

Annales UMCS, Mathematica

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 spectrum of Schrödinger operators with random δ magnetic fields

Takuya Mine, Yuji Nomura (2009)

Annales de l’institut Fourier

We shall consider the Schrödinger operators on ℝ 2 with the magnetic field given by a nonnegative constant field plus random δ 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 structure of disjoint iteration groups on the circle

Krzysztof Ciepliński (2004)

Czechoslovak Mathematical Journal

The aim of the paper is to investigate the structure of disjoint iteration groups on the unit circle 𝕊 1 , that is, families ℱ = { F v 𝕊 1 ⟶ 𝕊 1 v ∈ V } of homeomorphisms such that F v 1 ∘ F v 2 = F v 1 + v 2 , v 1 , v 2 ∈ V , and each F v either is the identity mapping or has no fixed point ( ( V , + ) is an arbitrary 2 -divisible nontrivial (i.e., c a r d V > 1 ) abelian group).

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