Positive real rational functions play a central role in both deterministic and stochastic linear systems theory, as well as in circuit synthesis, spectral analysis, and speech processing. For this reason, results about positive real transfer functions and their realizations typically have many applications and manifestations. In this paper, we study certain manifolds and submanifolds of positiv...

In this paper, we apply Nevanlinna theory to prove two Ax–Schanuel type theorems for functional transcendence when the original exponential map is replaced by other meromorphic functions. We give examples show that these results are optimal. As a byproduct, also analytic dependence implies algebraic certain classes of entire Finally, some links transcendental number and geometric theorem will b...

This article studies the existence and exact form of entire solutions several Fermat type partial differential equations in \(\mathbb{C}^2\), by utilizing Nevanlinna theory meromorphic functions complex variables. We obtain results about transcendental with finite order for some variations functional equations. Our are extensions generalizations previous theorems Xu Cao [29,30], Liu Dong [19].&...

We obtain a qualitatively new sufficient condition of nonnegativity for the coefficients power series inverse to with positive coefficients. In particular, we prove that element-wise product retains this property. generalizes classical Hardy–Kaluza theorem on series. These results are generalized case multivariable Results kind applied in Nevanlinna–Pick theory.

In the present paper we define quasimeromorphic mappings on homogeneous groups and study their properties. We prove an analogue of results of L. Ahlfors, R. Nevanlinna and S. Rickman, concerning the value distribution for quasimeromorphic mappings on H-type Carnot groups for parabolic and hyperbolic type domains. Introduction The classical value distribution theory for analytic functions w(z) s...

We develop a spectral factorization algorithm based on linear fractional transformations and on the Nevanlinna-Pick interpolation theory. The algorithm is recursive and depends on a choice of points (Zk, k 1, 2, ") inside the unit disk. Under a mild condition on the distribution of the zk's, the convergence of the algorithm is established. The algorithm is flexible and convergence can be influe...

Several integrability tests for discrete equations will be reviewed. All tests considered can be applied directly to a given discrete equation and do not rely on the a priori knowledge of the existence of related structures such as Lax pairs. Specifically, singularity confinement, algebraic entropy, Nevanlinna theory, Diophantine integrability and discrete systems over finite fields will be des...

We study certain sequences of rational functions with poles outside the unit circle. Such kind of sequences are recursively constructed based on sequences of complex numbers with norm less than one. In fact, such sequences are closely related to the Schur-Nevanlinna algorithm for Schur functions on the one hand and on the other hand to orthogonal rational functions on the unit circle. We shall ...

We consider 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 results related to the growth at the singularities ...