Related papers: Interpolation orbits in couples of Lebesgue spaces

Using the theory of quasiconformal mappings, we simplify the proof of the recent result by Taylor and Totik (see IMA Journal of Numerical Analysis 30 (2010) 462--486) on the behavior of the Lebesgue constants for interpolation points on a…

We construct a linear operator $T:\mathscr S'(\mathbb R^n)\to \mathscr S'(\mathbb R^n)$ such that $T:\mathscr B_{pq}^s(\mathbb R^n)\to\mathscr B_{pq}^s(\mathbb R^n)$ for all $0<p,q\le\infty$ and $s\in\mathbb R$, but $T(\mathscr…

Let S be an nXn real symmetric matrix with spectral decomposition S=Q^T Lambda Q, where Q is an orthogonal matrix and Lambda is diagonal with simple spectrum {lambda_1,..., lambda_n}. Also let O_S e R_S be the orbits by conjugation of S by,…

This paper addresses the $\mathcal{H}_2$-optimal approximation of linear dynamical systems with quadratic-output functions, also known as linear quadratic-output systems. Our major contributions are threefold. First, we derive…

The $\ell_2-$ and $\ell_1-$regularized modified Lagrange interpolation formulae over $[-1,1]$ are deduced in this paper. This paper mainly analyzes the numerical characteristics of regularized barycentric interpolation formulae, which are…

The first integrals of the Kepler problem are used to compute preliminary orbits starting from two short observed arcs of a celestial body, which may be obtained either by optical or radar observations. We write polynomial equations for…

This paper concerns the combinatorics of the orbit Hecke algebra associated with the orbit of a two sided Weyl group action on the Renner monoid of a finite monoid of Lie type, $M$. It is shown by Putcha in \cite{Putcha97} that the…

We give a detailed description of the local commutant approach to wavelet theory using operator algebraic methods. We include a new result on interpolation pairs of wavelet sets: Every pair in the generalized Journe family of wavelet sets…

We have used an existing, robotic, multi-lens, all-sky camera system, coupled to a dedicated data reduction pipeline, to automatically determine orbital parameters of satellites in Low Earth Orbit (LEO). Each of the fixed cameras has a…

Let (A_0,A_1) be a compatible couple of Banach spaces in the interpolation theory sense. We give a formula for the K_t-functional of the interpolation couples (l_1(A_0),c_0(A_1)) or (l_1(A_0),l_infinity(A_1)) and (L_1(A_0),L_infinity(A_1)).

This paper is devoted to the interpolation principle between spaces of weak type. We characterise interpolation spaces between two Marcinkiewicz spaces in terms of Hardy type operators involving suprema. We study general properties of such…

Let $ X=(X_0,X_1)$ and $ Y=(Y_0,Y_1)$ be Banach couples and suppose $T: X\to Y$ is a linear operator such that $T:X_0\to Y_0$ is compact. We consider the question whether the operator $T:[X_0,X_1]_{\theta}\to [Y_0,Y_1]_{\theta}$ is compact…

A method for 3D interpolation between hard spheres is described. The function to be interpolated could be the charge density between atoms in condensed matter. Its electrostatic potential is found analytically, and so are various integrals.…

Consider the restriction of an irreducible unitary representation $\pi$ of a Lie group $G$ to its subgroup $H$. Kirillov's revolutionary idea on the orbit method suggests that the multiplicity of an irreducible $H$-module $\nu$ occurring in…

This paper gives a systematic study of operator-valued local Hardy spaces. These spaces are localizations of the Hardy spaces defined by Tao Mei, and share many properties with Mei's Hardy spaces. We prove the ${\rm h}_1$-$\rm bmo$ duality,…

This paper investigates the well-posedness of linear elliptic equations, focusing on the divergence-free transformation introduced in the author's recent work [J. Math. Anal. Appl. 548 (2025), 129425]. By comparing this approach with…

In this paper we establish asymptotically best possible interpolation Lebesgue-type inequalities for $2\pi$-periodic functions $f$, which are representable as generalized Poisson integrals of the functions $\varphi$ from the space $L_p$,…

This paper discusses various aspects of the collection of unitary operators $CUC$, where $U$ is a fixed unitary operator on a complex Hilbert space $\mathcal{H}$ and $C$ varies over the set of all conjugations on $\mathcal{H}$ (antilinear,…

We investigate (twisted) rings of differential operators on the resolution of singularities of a particular irreducible component of the (Zarisky) closure of the minimal orbit $\bar O_{\mathrm{min}}$ of $\mathfrak{sp}_{2n}$, intersected…

Following ideas from the Abstract Interpolation Problem of Katsnelson et al. (Operators in spaces of functions and problems in function theory, vol 146, pp 83-69, Naukova Dumka, Keiv, 1987) for Schur class functions, we study a general…