Factoring the logarithmic spiral.
We give a complete characterization of the positive trigonometric polynomials on the bi-circle, which can be factored as where is a polynomial nonzero for and . The conditions are in terms of recurrence coefficients associated with the polynomials in lexicographical and reverse lexicographical ordering orthogonal with respect to the weight on the bi-circle. We use this result to describe how specific factorizations of weights on the bi-circle can be translated into identities relating...
MSC 2010: 30C45The universally prestarlike functions of order α ≤ 1 in the slit domain Λ = C [1;∞) have been recently introduced by S. Ruscheweyh. This notion generalizes the corresponding one for functions in the unit disk Δ (and other circular domains in C). In this paper, we obtain the coefficient inequalities and the Fekete-Szegö inequality for such functions.
In this paper, we obtain Fekete–Szegö inequalities for a generalized class of analytic functions for which (; ; ; ; ; ) lies in a region starlike with respect to and is symmetric with respect to the real axis.
The authors obtain the Fekete-Szegő inequality (according to parameters and in the region , and , or in the region and ) for certain normalized analytic functions belonging to which satisfy the condition Also certain...
MSC 2010: 30C45
In this paper, we estimate the Douglas-Dirichlet functionals of harmonic mappings, namely Euclidean harmonic mapping and flat harmonic mapping, by using the extremal dilatation of finite distortion functions with given boundary value on the unit circle. In addition, -Dirichlet functionals of harmonic mappings are also investigated.
We study Mellin transforms for which is periodic with period in order to investigate ‘flows’ of such functions to Riemann’s and the possibility of proving the Riemann Hypothesis with such an approach. We show that, excepting the trivial case where , the supremum of the real parts of the zeros of any such function is at least .We investigate a particular flow of such functions which converges locally uniformly to as , and show that they exhibit features similar to . For example, ...