In the present investigation, inspired by work on Yamaguchi type class of analytic functions satisfyingthe criteria $\mathfrak{Re}\{\frac{f (z)}{z}\} > 0, $ in openunit disk $\Delta=\{z \in \mathbb{C}\colon |z|<1\}$ and making use S\v{a}l\v{a}gean-difference operator, which is a special Dunkl operator with constant $\vartheta$ $\Delta$ , wedesignate definite new classes $\mathcal{R}_{\lam...

An intriguing correspondence between ingredients in geometric function theory related to the famous Bieberbach conjecture (de Branges' theorem) and non-perturbative crossing symmetric representation of 2-2 scattering amplitudes identical scalars is pointed out. Using dispersion relation unitarity, we are able derive several inequalities, analogous those which arise discussions conjecture. We ne...

In this paper we continue to explore the connection between tensor algebras and displacement structure. We focus on recursive orthonormalization and we develop an analogue of the Szegö type theory of orthogonal polynomials in the unit circle for several noncommuting variables. Thus, we obtain the recurrence equations and Christoffel-Darboux formulas for Szegö polynomials in several noncommuting...

We consider the time–continuous doubly–dispersive channel with additive Gaussian noise and establish a capacity formula for the case where the channel operator is represented by a symbol which is periodic in time and fulfills some further integrability, smoothness and oscillation conditions. More precisely, we apply the well–known HolsingerGallager model for translating a time–continuous channe...

We consider the problem of approximating a convex gure in the plane by a pair r R of homothetic that is similar and parallel rectangles with r C R We show the existence of such a pair where the sides of the outer rectangle are at most twice as long as the sides of the inner rectangle thereby solving a problem posed by P olya and Szeg o If the n vertices of a convex polygon C are given as a sort...

‎universally prestarlike functions of order $alphaleq 1$ in the‎ ‎slit domain $lambda=mathbb{c}setminus [1,infty)$ have been‎ ‎recently introduced by s‎. ‎ruscheweyh.this notion generalizes the‎ ‎corresponding one for functions in the unit disk $delta$ (and‎ ‎other circular domains in $mathbb{c}$)‎. ‎in this paper‎, ‎we obtain‎ ‎the fekete-szegö coefficient functional for transforms of such‎ ‎f...

Let p be a trigonometric polynomial, non-negative on the unit circle T. We say that a measure σ on T belongs to the polynomial Szeg˝ o class, if dσ(e iθ) = σ ′ ac (e iθ)dθ + dσ s (e iθ), σ s is singular, and 2π 0 p(e iθ) log σ ′ ac (e iθ) dθ > −∞ For the associated orthogonal polynomials {ϕ n }, we obtain pointwise asymp-totics inside the unit disc D. Then we show that these asymptotics hold in...

A new approach to the computation of the poles of a stable autoregressive system from the reeection coeecients is proposed. Equivalently, we compute the zeros of Szeg} o polynomials from the associated Schur parameters. The numerical method utilizes an eecient algorithm for computing the (unimodular) zeros of a unitary Hessenberg matrix; this step can be regarded as the computation of the poles...