The method of convolution is used to determine a sharp condition for starlikeness of analytic functions defined in the unit disc U = {z ∈ ℂ: |z| < 1} and having the property f(0) = f'(0) - 1 = 0. The integral version is given using the Alexander integral operator.
Due to the fact that in the case the -Bernstein polynomials are no longer positive linear operators on the study of their convergence properties turns out to be essentially more difficult than that for In this paper, new saturation theorems related to the convergence of -Bernstein polynomials in the case are proved.
This paper provides sufficient conditions on a quasisymmetric automorphism γ of the unit circle which guarantee the existence of the smallest positive eigenvalue of γ. They are expressed by means of a regular quasiconformal Teichmüller self-mapping φ of the unit disc Δ. In particular, the norm of the generalized harmonic conjugation operator is determined by the maximal dilatation of φ. A characterization of all eigenvalues of a quasisymmetric automorphism γ in terms of the smallest positive eigenvalue...
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 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).
In [Comput. Math. Appl. 41 (2001), 135--147], A. A. Ungar employs the Möbius gyrovector spaces for the introduction of the hyperbolic trigonometry. This Ungar's work plays a major role in translating some theorems from Euclidean geometry to corresponding theorems in hyperbolic geometry. In this paper we explore the theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry.