For r > 0 let r {z ∈ : |z| < r}. Let 1 . Let the functions f and F be analytic in the unit disc . A function f is called subordinate to F, written f ≺ F, if F is univalent in , f 0 F 0 and f ⊂ F . Let D be a domain in 2 and ψ : 2 ⊃ D → be an analytic function, and let p be a function analytic in with p z , zp′ z ∈ D, z ∈ and h be a function analytic and univalent in . The function p is said to ...

In this paper, we define and investigate a new class of bi-Bazilevic functions related to shell-like curves connected with Fibonacci numbers.  Furthermore, we find estimates of first two coefficients of functions belonging to this class. Also, we give the Fekete-Szegoinequality for this function class.

We show that a correct use of the Wigner Distribution (WD) for time-frequency signal analysis requires use of the analytic signal. This version, often referred to as the Wigner-Ville Distribution (WVD), is straightforward to compute, does not exhibit any aliasing problem, and introduces no frequency artifacts. The problems introduced by the use of the Wigner Distribution with a real signal are ...

A fractal function is a function whose graph is the attractor of an iterated function system. This paper generalizes analytic continuation of an analytic function to continuation of a fractal function.

Data clustering is a combinatorial optimization problem. This article shows that clustering is also an optimization problem for an analytic function. The mean squared error, or in this case, the squared error can expressed as an analytic function. With an analytic function we benefit from the existence of standard optimization methods: the gradient of this function is calculated and the descent...

In this paper some new positive results in the Operator Corona Problem are obtained in rather general situation. The main result is that under some additional assumptions about a bounded analytic operator-valued function F in the unit disc D the condition F (z)F (z) ≥ δI ∀z ∈ D (δ > 0) implies that F has a bounded analytic left inverse. Typical additional assumptions are (any of the following):...

In this work we study the Positive Extension (PE) property and Hilbert’s 17th Problem for real analytic germs and sets. A real analytic germ Xo of Ro has the PE property if every positive semidefinite analytic function germ on Xo has a positive semidefinite analytic extension to Ro ; analogously one states the PE property for a global real analytic set X in an open set Ω of R. These PE properti...

Let Ω be a bounded, weakly pseudoconvex domain in Cn, n ≥ 2, with real-analytic boundary. A real-analytic submanifold M ⊂ ∂Ω is called an analytic interpolation manifold if every real-analytic function on M extends to a function belonging to O(Ω). We provide sufficient conditions for M to be an analytic interpolation manifold. We give examples showing that neither of these conditions can be rel...