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...

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...

In this paper, we define new subclasses ${S}^{*}_{q}(alpha,Phi),$ ${M}_{q}(alpha,Phi)$ and ${L}_{q}(alpha,Phi)$ of analytic functions in the space of logistic sigmoid functions based on quasi--subordination and determine the initial coefficient estimates $|a_2|$ and $|a_3|$ and also determine the relevant connection to the classical Fekete--Szeg"o inequalities. Further, we discuss the improved ...

In this paper, we give an upper bound of Hankel determinant (H2(1)) for the classes M(?), ? C. Also, obtain a sharp estimate classical Fekete-Szeg? inequality. That is, will get H2(1) = c3 c22. Moreover, in class analytic functions on unit disc, assuming existence angular limit boundary point, estimations below modulus derivative have been obtained.

We study the properties of stationary G-chains in terms their generating functions. In particular, we prove an analogue Szeg\H{o} limit theorem for symplectic eigenvalues, derive expression entropy rate quantum Gaussian processes, and distribution eigenvalues truncated block Toeplitz matrices. also introduce a concept numerical range, analogous to that some its basic properties, mainly context ...

We study, for all p > 0 the asymptotic behavior of Lp extremal polynomials with respect to measure ? = + ?, denotes a positive whose support is unit circle plus denumerable set mass points, which accumulate at and satisfy Blaschke?s condition ?a ?s, ?s absolutely continuous part satisfies Szeg? singular part. Our main result explicit strong formulas polynomials.

‎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...

The aim of this study is to solve the Fekete-Szeg? problem and define upper bound for Hankel determinant H2(1) in a novel class K analytical functions unit disc. Moreover, analytic on disc, assuming existence an angular limit boundary point, estimations from below modulus derivative have been obtained.