Page 1 Next

Displaying 1 – 20 of 42

Showing per page

Fejér–Riesz factorizations and the structure of bivariate polynomials orthogonal on the bi-circle

Jeffrey S. Geronimo, Plamen Iliev (2014)

Journal of the European Mathematical Society

We give a complete characterization of the positive trigonometric polynomials Q ( θ , ϕ ) on the bi-circle, which can be factored as Q ( θ , ϕ ) = | p ( e i θ , e i ϕ ) | 2 where p ( z , w ) is a polynomial nonzero for | z | = 1 and | w | 1 . The conditions are in terms of recurrence coefficients associated with the polynomials in lexicographical and reverse lexicographical ordering orthogonal with respect to the weight 1 4 π 2 Q ( θ , ϕ ) 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...

Fekete-Szegö Inequality for Universally Prestarlike Functions

Shanmugam, T., Lourthu Mary, J. (2010)

Fractional Calculus and Applied Analysis

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.

Fekete–Szegö Problem for a New Class of Analytic Functions Defined by Using a Generalized Differential Operator

M. K. Aouf, R. M. El-Ashwah, A. A. M. Hassan, A. H. Hassan (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper, we obtain Fekete–Szegö inequalities for a generalized class of analytic functions f ( z ) 𝒜 for which 1 + 1 b z D α , β , λ , δ n f ( z ) ' D α , β , λ , δ n f ( z ) - 1 ( α , β , λ , δ 0 ; β > α ; λ > δ ; b * ; n 0 ; z U ) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis.

Fekete-Szegő problem for subclasses of generalized uniformly starlike functions with respect to symmetric points

Nihat Yagmur, Halit Orhan (2014)

Mathematica Bohemica

The authors obtain the Fekete-Szegő inequality (according to parameters s and t in the region s 2 + s t + t 2 < 3 , s t and s + t 2 , or in the region s 2 + s t + t 2 > 3 , s t and s + t 2 ) for certain normalized analytic functions f ( z ) belonging to k -UST λ , μ n ( s , t , γ ) which satisfy the condition ( s - t ) z ( D λ , μ n f ( z ) ) ' D λ , μ n f ( s z ) - D λ , μ n f ( t z ) > k ( s - t ) z ( D λ , μ n f ( z ) ) ' D λ , μ n f ( s z ) - D λ , μ n f ( t z ) - 1 + γ , z 𝒰 . Also certain...

Finite distortion functions and Douglas-Dirichlet functionals

Qingtian Shi (2019)

Czechoslovak Mathematical Journal

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.

Flows of Mellin transforms with periodic integrator

Titus Hilberdink (2011)

Journal de Théorie des Nombres de Bordeaux

We study Mellin transforms N ^ ( s ) = 1 - x - s d N ( x ) for which N ( x ) - x is periodic with period 1 in order to investigate ‘flows’ of such functions to Riemann’s ζ ( s ) and the possibility of proving the Riemann Hypothesis with such an approach. We show that, excepting the trivial case where N ( x ) = x , the supremum of the real parts of the zeros of any such function is at least 1 2 .We investigate a particular flow of such functions { N λ ^ } λ 1 which converges locally uniformly to ζ ( s ) as λ 1 , and show that they exhibit features similar to ζ ( s ) . For example, N λ ^ ( s ) ...

Currently displaying 1 – 20 of 42

Page 1 Next