We prove a limit theorem connected to graphs, which when the graph is a cycle reduces to Szego's theorem for the trace of a product of Toeplitz matrices. The main tool used is a Holder type inequality for multiple integrals of functions which are applied to variables satisfying linear dependency relations.

It is shown that a conjecture of E.A. Rakhmanov is true concerning the zero distribution of orthogonal polynomials with respect to a measure having a discrete real support. We also discuss the case of extremal polynomials with respect to some discrete L p {norm, 0 < p 1, and give an extension to complex supports. Furthermore, we present properties of weighted Fekete points with respect to discr...

In this paper, we consider a class L (λ, μ;φ) of analytic functions f defined in the open unit disk U satisfying the subordination condition that q(z) Df(z) Dλf(z) ≺ φ(z) (λ ∈ N0, μ ≥ 0; z ∈ U), where q(z) = ( z Dλf(z) )μ−2 , D is the Sălăgean operator and φ(z) is a convex function with positive real part in U. We obtain some characteristic properties giving the coefficient inequality, radius a...

The Szego projection preserves global smoothness in weakly pseudoconvex domains that are regular in the sense of Diederich, Fornaess, and Catlin. It preserves local smoothness near boundary points of finite type. The Bergman projection, being linked to the 3 problem, plays an important role in several complex variables, as demonstrated by recent applications to the boundary behavior of holomorp...

For λ ≥ 0 and 0 ≤ α < 1 < β, we denote by K (λ;α, β) the class of normalized analytic functions satisfying the two sided-inequality α << ( z f ′(z) f (z) + λ z2 f ′′(z) f (z) ) < β (z ∈ U), where U is the open unit disk. Let KΣ(λ;α, β) be the class of bi-univalent functions such that f and its inverse f −1 both belong to the class K (λ;α, β). In this paper, we establish bounds for the coefficie...

In this article, we establish the bounds for initial Taylor–Maclaurin coefficients |a2| and |a3| a new family G?(?,?,?;h) of holormorphic bi-univalent functions which involve prestarlike functions. Furthermore, investigate Fekete–Szegö type inequality, special cases consequences.

Based on a Wold decomposition for families of partial isometries and projections of Cuntz-Krieger-Toeplitz-type, we extend several fundamental theorems from the case of single vertex graphs to the general case of countable directed graphs with no sinks. We prove a Szego-type factorization theorem for CKT families, which leads to information on the structure of the unit ball in free semigroupoid...