Related papers: Convex Cones of Generalized Positive Rational Func…

Nevanlinna-Pick interpolation developed from a topic in classical complex analysis to a useful tool for solving various problems in control theory and electrical engineering. Over the years many extensions of the original problem were…

We here extend the well known Positive Real Lemma (also known as the Kalman-Yakubovich-Popov Lemma) to complex matrix-valued generalized positive rational function, when non-minimal realizations are considered. We then exploit this result…

Positive real odd matrix functions, often referred to as positive real lossless matrix functions, play an important role in many applications in multi-port electrical systems. In this paper we present closer analogues to some of the known…

In this paper we obtain a noncommutative multivariable analogue of the classical Nevanlinna-Pick interpolation problem for analytic functions with positive real parts on the open unit disc. As consequences, we deduce some results concerning…

Using polynomial interpolation, along with structural properties of the family of positive real rational functions, we here show that a set of m nodes in the open left half of the complex plane, can always be mapped to anywhere in the…

A normalized univalent function is uniformly convex if it maps every circular arc contained in the open unit disk with center in it into a convex curve. This article surveys recent results on the class of uniformly convex functions and on…

We introduce the notion of one-sided mapping cones of positive linear maps between matrix algebras. These are convex cones of maps that are invariant under compositions by completely positive maps from either the left or right side. The…

In the paper, we introduce the generalized convex function on fractal sets of real line numbers and study the properties of the generalized convex function. Based on these properties, we establish the generalized Jensen inequality and…

New classes of generalized Nevanlinna functions, which under multiplication with an arbitrary fixed symmetric rational function remain generalized Nevanlinna functions, are introduced. Characterizations for these classes of functions are…

For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.

The classical perspective of a function is a construction which transforms a convex function into one that is jointly convex with respect to an auxiliary scaling variable. Motivated by applications in several areas of applied analysis, we…

The conic structure of the convex cone of non-negative operator convex functions on $(0,\infty)$ (also on $(-1,1)$) is clarified. We completely determine the extreme rays, the closed faces, and the simplicial closed faces of this convex…

A natural interpolation problem in the cone of positive harmonic functions is considered and the corresponding interpolating sequences are geometrically described.

A generalized Nevanlinna function $Q(z)$ with one negative square has precisely one generalized zero of nonpositive type in the closed extended upper halfplane. The fractional linear transformation defined by $Q_\tau(z)=(Q(z)-\tau)/(1+\tau…

In the paper we consider convex cones in infinite-dimensional real vector spaces which are endowed with no topology. The main purpose is to study an internal geometric structure of convex cones and to obtain an analytical description of…

We consider simple rational functions $R_{mn}(x)=P_m(x)/Q_n(x)$, with $P_m$ and $Q_n$ polynomials of degree $m$ and $n$ respectively. We look for "nice" functions, which we define to be ones where as many as possible of the roots, poles,…

Functions with uniform level sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used, e.g., in multicriteria optimization, decision theory, mathematical…

This paper considers projection and convolution operations for integrally convex functions, which constitute a fundamental function class in discrete convex analysis. It is shown that the class of integrally convex functions is stable under…

We introduce two kinds of generalized $s$-convex functions on real linear fractal sets $\mathbb{R}^{\alpha}(0<\alpha<1)$. And similar to the class situation, we also study the properties of these two kinds of generalized $s$-convex…

We give a characterization for the existence of a holomorphic interpolant on the unit polydisc $\mathbb{D}^n,$ $n\geq 2,$ for prescribed three-point Pick--Nevanlinna data. One of the key steps is a characterization for the existence of an…