Related papers: Multivariate orthogonal spline systems

Finite trigonometric Fourier series on a set of discrete equidistant points are considered. A finite system of orthogonal functions that have interpolation and certain differential properties on the period is introduced. Finite Fourier…

Let $\Omega \subset \mathbb{R}^d$ be a bounded open set containing zero, $s \in (0,1)$ and $p \in (1, \infty)$. In this paper, we first deal with the existence, non-existence and some properties of ground-state solutions for the following…

Let $\mathcal{M}$ be a von Neumann algebra with a normal semifinite faithful trace $\tau$. We prove that every continuous $m$-homogeneous polynomial $P$ from $L^p(\mathcal{M},\tau)$, with $0<p<\infty$, into each topological linear space $X$…

We obtain order estimates for the best uniform orthogonal trigonometric approximations of $2\pi$-periodic functions, whose $(\psi,\beta)$-derivatives belong to unit balls of spaces $L_{p}, \ 1\leq p<\infty$, in case at consequences…

In this paper we come up with a dual version of the Furstenberg problem and obtain partial results via $L^p$ estimates of orthogonal projections. Examples are also discussed. Moreover, compared with general sets, we find that special…

We propose a semiparametric family of copulas based on a set of orthonormal functions and a matrix. This new copula permits to reach values of Spearman's Rho arbitrarily close to one without introducing a singular component. Moreover, it…

A uniformly bounded complete orthonormal system of functions $\Theta =\{ \theta_n\}_{n=1}^{\infty},$ $ \|\theta_n\|_{L^\infty_{[0,1]} } \leq M $ is constructed such that $\sum_{n=1}^{\infty} a_{n}\theta_{n}$ converges almost everywhere on…

The class of problems treated here are elliptic partial differential equations with a homogeneous boundary condition and a non-linear perturbation obtained by composition with a fixed smooth function. The existence of solutions is obtained…

We consider convex optimization problems with the objective function having Lipshitz-continuous $p$-th order derivative, where $p\geq 1$. We propose a new tensor method, which closes the gap between the lower…

Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.

The orthogonal decomposition factorizes a tensor into a sum of an orthogonal list of rankone tensors. We present several properties of orthogonal rank. We find that a subtensor may have a larger orthogonal rank than the whole tensor and…

We construct a new class of multipartite states possessing orthogonal symmetry. This new class defines a convex hull of multipartite states which are invariant under the action of local unitary operations introduced in our previous paper…

We derive a formula which is a lower bound on the dimension of trivariate splines on a tetrahedral partition which are continuously differentiable of order $r$ in large enough degree. While this formula may fail to be a lower bound on the…

We interpret the Cuntz-Pimsner covariance condition as a nondegeneracy condition for representations of product systems. We show that Cuntz-Pimsner algebras over Ore monoids are constructed through inductive limits and section algebras of…

Let $d\in\mathbb N$ and $f$ be a function in the Orlicz class $L(\log^+L)^{d-1}$ defined on the unit cube $[0,1]^d$ in $\mathbb{R}^d$. Given partitions $\Delta_1,\ldots,$ $\Delta_d$ of $[0,1]$, we first prove that the orthogonal projection…

A sharp estimation of the $L^p$-norms of some matrix coefficients of the square integrable representations is conjectured. The conjecture can be proved for integer values of $p$ using a result of J. Burbea.

We study here systems of symmetries on $|1|$--graded parabolic geometries. We are interested in smooth systems of symmetries and we discuss non--flat homogeneous $|1|$--graded geometries. We show the existence of an invariant admissible…

In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…

Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in…

We consider controllability for divergence-free systems that have a conserved quantity and satisfy a H\"ormander condition. It is shown that such systems are controllable, provided that the conserved quantity is a proper function. The proof…