Related papers: The Multivariate Herglotz-Nevanlinna Class: Superr…
We consider an $n\times n$ linear system of ODEs with an irregular singularity of Poincar\'e rank 1 at $z=\infty$, holomorphically depending on parameter $t$ within a polydisc in $\mathbb{C}^n$ centred at $t=0$. The eigenvalues of the…
This is a study of a class of nonlocal nonlinear diffusion equations. We present a strong maximum principle for nonlocal time-dependent Dirichlet problems. Results are for bounded functions of space, rather than (semi)-continuous functions.…
We first give an exposition on holomorphic isometries from the Poincar\'e disk to polydisks and from the Poincar\'e disk to the product of the Poincar\'e disk with a complex unit ball. As an application, we provide an example of proper…
We show that for any closed surface of genus greater than one and for any finite weighted graph filling the surface, there exists a hyperbolic metric which realizes the least Dirichlet energy harmonic embedding of the graph among a fixed…
The main result of the present paper is the construction of fundamental solutions for a class of multidimensional elliptic equations with three singular coefficients, which could be expressed in terms of a confluent hypergeometric function…
An algebraic soliton of the massive Thirring model (MTM) is expressed by the simplest rational solution of the MTM with the spatial decay of $\mathcal{O}(x^{-1})$. The corresponding potential is related to a simple embedded eigenvalue in…
We prove existence and uniqueness of a solution of the Dirichlet problem for separately $(\alpha, \beta)$ - harmonic functions on the unit polydisc $\mathbb D^n$ with boundary data in $C(\mathbb T^n)$ using $(\alpha, \beta)$ - Poisson…
Contour-integral-based rational filter leads to interior eigensolvers for non-Hermitian generalized eigenvalue problems. Based on Zolotarev's third problem, this paper proves the asymptotic optimality of the trapezoidal quadrature of the…
The Bessmertny\u{\i} class consists of rational matrix-valued functions of $d$ complex variables representable as the Schur complement of a block of a linear pencil $A(z)=z_1A_1+\cdots+z_dA_d$ whose coefficients $A_k$ are positive…
Multiresolution analysis of electronic structure affords the opportunity to capture the full physics of atomic cores in a systematically improvable manner. Applying new techniques, we demonstrate for the first time that multiresolution…
We establish the existence of a finite-dimensional unitary realization for every matrix-valued rational inner function from the Schur--Agler class on a unit square-matrix polyball. In the scalar-valued case, we characterize the denominators…
This paper presents algorithms for solving multiobjective integer programming problems. The algorithm uses Barvinok's rational functions of the polytope that defines the feasible region and provides as output the entire set of nondominated…
A theorem is proved concerning approximation of analytic functions by multivariate polynomials in the $s$-dimensional hypercube. The geometric convergence rate is determined not by the usual notion of degree of a multivariate polynomial,…
A common strategy in the numerical solution of partial differential equations is to define a uniform discretization of a tensor-product multi-dimensional logical domain, which is mapped to a physical domain through a given coordinate…
In this paper, we prove that nonnegative polyharmonic functions on the upper half space satisfying a conformally invariant nonlinear boundary condition have to be the "\emph{polynomials} plus \emph{bubbles}" form. The nonlinear problem is…
The nondegenerate Nevanlinna-Pick-Carath\'eodory-Fejer interpolation problem with finitely many interpolation conditions always has infinitely many solutions in a generalized Schur class $\cS_\kappa$ for every $\kappa\ge \kappa_{\rm min}$…
We introduce the notion of rationality for hyperholomorphic functions (functions in the kernel of the Cauchy-Fueter operator). Following the case of one complex variable, we give three equivalent definitions: the first in terms of…
The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…
For each n,N>0 we construct a set of points x_1,...,x_M in D^n with the following property: if f is a rational inner function on D^n of degree strictly less than N and g is an analytic function mapping D^n to D that satisfies g(x_i)=f(x_i)…
Functions with singularities are notoriously difficult to approximate with conventional approximation schemes. In computational applications, they are often resolved with low-order piecewise polynomials, multilevel schemes, or other types…