Related papers: A construction of linear bounded interpolatory ope…

The concepts of evaluation and interpolation are extended from univariate skew polynomials to multivariate skew polynomials, with coefficients over division rings. Iterated skew polynomial rings are in general not suitable for this purpose.…

We show that if a 1-hyperbolic structurally finite entire function of type $(p,q)$, $p\ge 1$, is linearizable at an irrationally indifferent fixed point, then its multiplier satisfies the Brjuno condition. We also prove the generalized…

This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…

This paper introduces a new framework for constructing the Discrete Empirical Interpolation Method DEIM projection operator. The interpolation node selection procedure is formulated using the QR factorization with column pivoting, and it…

We propose a q-deformation of the su(2)-invariant Schrodinger equation of a spinless particle in a central potential, which allows us not only to determine a deformed spectrum and the corresponding eigenstates, as in other approaches, but…

In this paper we focus on the unconstrained binary quadratic optimization model, maximize x^t Qx, x binary, and consider the problem of identifying optimal solutions that are robust with respect to perturbations in the Q matrix.. We are…

The intertwining operator constructed in [Sz1,Sz2] does not appear in the right form. It is established there by using only the anticommutators. The correct operator must involve all endomorphisms, which are unified by the Z-Fourier…

Let $m(\xi,\eta)$ be a measurable locally bounded function defined in $\mathbb R^2$. Let $1\leq p_1,q_1,p_2,q_2<\infty $ such that $p_i=1$ implies $q_i=\infty $. Let also $0<p_3,q_3<\infty $ and $1/p=1/p_1+1/p_2-1/p_3$. We prove the…

It follows from the Marcus-Spielman-Srivastava proof of the Kadison-Singer conjecture that if $G=(V,E)$ is a $\Delta$-regular dense expander then there is an edge-induced subgraph $H=(V,E_H)$ of $G$ of constant maximum degree which is also…

Let $V$ be a vector space of dimension $N$ over the finite field $\mathbb{F}_q$ and $T$ be a linear operator on $V$. Given an integer $m$ that divides $N$, an $m$-dimensional subspace $W$ of $V$ is $T$-splitting if $V=W\oplus TW\oplus…

The paper deals with two fundamental types of trigonometric polynomials and splines on uniform grids, which allow us to construct interpolation approximations that depend linearly on the values of the interpolated function. Fundamental on…

We study an inverse drift problem for a two-dimensional parabolic equation on the unit square with mixed boundary conditions, where the drift coefficient is recovered from terminal observation data $g=u(\cdot,T)$. A monotone operator is…

In this paper, a new class of \emph{Taylor-accelerated neural network interpolation operators} is introduced on quasi-uniform irregular grids. These operators improve existing neural network interpolation operators by incorporating Taylor…

In this paper we investigate the boundedness properties of bilinear multiplier operators associated with unimodular functions of the form $m(\xi,\eta)=e^{i \phi(\xi-\eta)}$. We prove that if $\phi$ is a $C^1(\mathbb R^n)$ real-valued…

In this document I develop a weight function theory of positive order basis function interpolants and smoothers. **In Chapter 1 the basis functions and data spaces are defined directly using weight functions. The data spaces are used to…

We establish new properties of inhomogeneous spin $q$-Whittaker polynomials, which are symmetric polynomials generalizing $t=0$ Macdonald polynomials. We show that these polynomials are defined in terms of a vertex model, whose weights come…

This paper constructs (with challenging obstacles) on the three torus with its cubical decomposition: Firstly, a combinatorial graded intersection algebra (graded by the codimension) which is commutative and associative defined by…

The perimeter and area generating functions of exactly solvable polygon models satisfy q-functional equations, where q is the area variable. The behaviour in the vicinity of the point where the perimeter generating function diverges can…

A function is called quasiperiodic if its fundamental frequencies are linearly independent over the rationals. With appropriate parameters, the sliding window point clouds of such functions can be shown to be dense in tori with dimension…

In this paper, we construct a Durrmeyer-type variant of Gr\"unwald interpolation operators on the space $L^p[0,{\pi}]$. We prove their fundamental properties, including boundedness and convergence in the $L^p$-norm. We establish the…