The nondegenerate Nevanlinna-Pick-Carathéodory-Fejer interpolation problem with finitely many interpolation conditions always has infinitely many solutions in a generalized Schur class Sκ for every κ ≥ κmin where the integer κmin equals the number of negative eigenvalues of the Pick matrix associated to the problem and completely determined by interpolation data. A linear fractional description...

In this paper, we derive a new fast algorithm for the matrixvalued Nevanlinna-Pick interpolation. Given n distinct points zi in the unit disk jzj < 1 and n complex matrices Wk of dimension m m, satisfying the Pick condition for 1 k n, the new Nevanlinna-Pick interpolation algorithm requires only 20 3 nm 3 complex arithmetic operations to evaluate the matrix-valued interpolatory rational functio...

An interpolation problem of Nevanlinna-Pick type for complexvalued Schur functions in the open unit disk is considered. We prescribe the values of the function and its derivatives up to a certain order at finitely many points. Primarily, we study the case that there exist many Schur functions fulfilling the required conditions. For this situation, an application of the theory of orthogonal rati...

It is shown that, if f is a meromorphic function of order zero and q ∈ C, then m „ r, f(qz) f(z) « = o(T (r, f)) (‡) for all r on a set of logarithmic density 1. The remainder of the paper consist of applications of identity (‡) to the study of value distribution of zero-order meromorphic functions, and, in particular, zero-order meromorphic solutions of q-difference equations. The results obta...

During the past years Lindquist and coworkers have formulated and studied the so called generalized maximum entropy problem. It generalizes the maximum entropy problem and thus includes problem like the Carathéodory extension problem and the Nevanlinna-Pick interpolation problem. A central ingredient in the theory is the dual (in mathematical programming sense) convex optimization problem. This...

In this paper, by using the Beurling-Nevanlinna type inequality we obtain new results on the existence of solutions of the Dirichlet problem with respect to the Schrödinger-prey operator. Meanwhile, the local stability of the Schrödingerean equilibrium and endemic equilibrium of the model are also discussed. We specially analyze the existence and stability of the Schrödingerean Hopf bifurcation...

We describe the real quasi-exactly solvable spectral locus of the PT-symmetric quartic using the Nevanlinna parametrization. MSC: 81Q05, 34M60, 34A05.

We obtain necessary and sufficient conditions for NevanlinnaPick interpolation on the unit disk with the additional restriction that all analytic interpolating functions satisfy f ′(0) = 0. Alternatively, these results can be interpreted as interpolation results for H∞(V ), where V is the intersection of the bidisk with an algebraic variety. We use an analysis of C*-envelopes to show that these...

We shall assume that reader is familiar with the fundamental results and the standard notations of the Nevanlinna value distribution theory of meromorphic functions(see [11,14]). In addition, we will use the notation σ(f) to denote the order of growth of entire function f(z), σ2(f) to denote the hyper-order of f(z), λ(f)(λ2(f)) to denote the exponent(hyper-exponent) of convergence of the zero-s...