Recent results of Davidson-Paulsen-Raghupathi-Singh give necessary and sufficient conditions for the existence of a solution to the NevanlinnaPick interpolation problem on the unit disk with the additional restriction that the interpolant should have the value of its derivative at the origin equal to zero. This concrete mild generalization of the classical problem is prototypical of a number of...

By using the Nevanlinna theory of value distribution, we investigate the existence of solutions of some types of non-linear q-difference differential equations. In particular, we generalize the Rellich-Wittich-type theorem and Malmquist-type theorem about differential equations to the case of q-difference differential equations (system).

We consider indeterminate rational moment problems on the real line with their associated orthogonal rational functions. There exists a Nevanlinna type parameterization relating to the problem, with associated Nevanlinna matrices of functions having singularities in the closure of the set of poles of the rational functions belonging to the problem. We prove that the growth at the isolated singu...

We propose a modification of the famous step-by-step process of solving the Nevanlinna-Pick problems for Nevanlinna functions. The process in question gives rise to three-term recurrence relations with coefficients depending on the spectral parameter. These relations can be rewritten in the matrix form by means of two Jacobi matrices. As a result of the considered approach, we prove a convergen...

Classical MD data on the dynamic charge-charge structure factor Szz(k, ω) of semi-quantal hydrogen plasmas modelled in [1] are revisited using the sum rules and other exact relations to reconstruct the system loss function, and the method of effective potentials to estimate its static characteristics. Introduction Classical molecular dynamics (MD) simulations of model hydrogen plasmas were carr...

For a rational tower, i.e., a composition sequence of rational maps, in addition to the algebraic and dynamical exceptional sets, various Nevanlinna theoretical exceptional sets are defined, and as we showed previously in the case of iterations, all of them are the same. In this paper, we extend this result to the cases of a rational tower with summable distortions and a finitely generated rati...

How can a complex curve be placed in a complex surface? The question is vague; many different ways to make it more specific may be imagined. The theory of deformations of complex structure, and their associated moduli spaces, is one way. Differential geometry and function theory, curvatures and currents, could be brought in. Even the generalized Nevanlinna theory of value distribution, for anal...