Related papers: Inner functions and Pick-Nevanlinna interpolation …

Every rational Nevanlinna function in n variables is a Cayley inner function in n + 1 variables with one variable fixed in the upper half-plane.

Using the notion of multivariate lower set interpolation, we construct nodal basis functions for the serendipity family of finite elements, of any order and any dimension. For the purpose of computation, we also show how to express these…

In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data…

Let $I$ be an inner function in the unit disk $\mathbb D$ and let $\mathcal N$ denote the Nevanlinna class. We prove that under natural assumptions, Bezout equations in the quotient algebra $\mathcal N/I\mathcal N$ can be solved if and only…

The synthesis of optimization algorithms typically follows a design-first-analyze-later approach, which often obscures fundamental performance limitations and hinders the systematic design of algorithms operating at the achievable…

This note comprises a synthesis of certain results in the theory of exact interpolation between Hilbert spaces. In particular, we examine various characterizations of interpolation spaces and their relations to a number of results in…

We consider optimal interpolation of functions analytic in simply connected domains in the complex plane. By choosing a specific structure for the approximant, we show that the resulting first order optimality conditions can be interpreted…

We give a short survey on plurisubharmonic interpolation, with focus on possibility of connecting two given plurisubharmonic functions by plurisubharmonic geodesic.

Let X be a countably infinite set of real numbers and let Y_x, x \in X, be an independent family of stationary random subsets of the real numbers, e.g. homogeneous Poisson point processes. We give criteria for the a.s. existence of various…

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

In this paper we present a construction of interpolatory Hermite multiwavelets for functions that take values in nonlinear geometries such as Riemannian manifolds or Lie groups. We rely on the strong connection between wavelets and…

We establish some multivariate generalizations of the Beurling-Lax-Halmos theorem.

The main goal of this article is to present several quadratic refinements and reverses of the well known Heinz inequality, for numbers and matrices, where the refining term is a quadratic function in the mean parameters. The proposed idea…

In this paper, we present the solution to Kolmogorov's problem for the classes of multiply monotone and completely monotone functions together with its connections to the Markov moment problem, Hermite-Birkhoff interpolation problem, and…

We introduce a family of piecewise-exponential functions that have the Hermite interpolation property. Our design is motivated by the search for an effective scheme for the joint interpolation of points and associated tangents on a curve…

The main object of this paper is to construct a new generating function of the (q-) Bernstein type polynomials. We establish elementary properties of this function. By using this generating function, we derive recurrence relation and…

Using factorisation and Arov-Krein inequality results, we derive important inequalities (in terms of $S$-nodes) in interpolation problems.

In this paper, we consider the structure-preserving model order reduction problem for multi-input/multi-output bilinear control systems by tangential interpolation. We propose a new type of tangential interpolation problem for structured…

In this paper we study the Nevanlinna-Pick matrix interpolation problem in the Carath\'eodory class with infinite data (both in the nondegenerate and degenerate cases). We develop the Sz\"okefalvi-Nagy and Kor\'anyi operator approach to…

Based on tensor neural network, we propose an interpolation method for high dimensional non-tensor-product-type functions. This interpolation scheme is designed by using the tensor neural network based machine learning method. This means…