Related papers: Interpolation Theorems in Harmonic Analysis

Recently, the extrapolation theory has become a mainsteam method to investigate some integral type operators, since it does not depend on the density of spaces. The purpose of this paper is threefold. The first is to establish product…

We introduce the basic concepts related to subharmonic functions and potentials, mainly for the case of the complex plane and prove the Riesz decomposition theorem. Beyond the elementary facts of the theory we deviate slightly from the…

This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…

This expository article explores the vital role of interpolation theory and Lorentz spaces in the rigorous analysis of partial differential equations (PDEs). While classical Lebesgue spaces ($L_{p}$) successfully measure the magnitude of…

This paper can be considered as the sequel of [6], where the authors have proposed an abstract construction of Hardy spaces H^1. They shew an interpolation result for these Hardy spaces with the Lebesgue spaces. Here we describe a more…

We prove a complex formulation of the real interpolation method, showing that the real and complex interpolation methods are not inherently real or complex. Using this complex formulation, we prove Stein interpolation for the real…

In a Euclidean Jordan algebra $V$ of rank $n$ which carries the trace inner product, to each element $a$ we associate the eigenvalue vector $\lambda(a)$ in $R^n$ whose components are the eigenvalues of $a$ written in the decreasing order.…

The main content of this paper is Lectures 5 and 6 that continue lecture notes [20]. Content of Lectures 1-4 of [20] is reviewed for the reader's convenience in sections 1-4, respectively. It is shown in Lecture 5 how residual parts of the…

We prove some interpolation inequalities which arise in the analysis of pattern formation in physics. They are the strong version of some already known estimates in weak form that are used to give a lower bound of the energy in many…

The subject of Chapter 1 is GKK $\tau$-matrices and related topics. Chapter 2 is devoted to boundedly invertible collections of matrices, with applications to operator norms and spline approximation. Various structured matrices (Toeplitz,…

An algorithm for generating interpolants for formulas which are conjunctions of quadratic polynomial inequalities (both strict and nonstrict) is proposed. The algorithm is based on a key observation that quadratic polynomial inequalities…

This book is an introduction to the nascent field of Fourier analysis on polytopes, and cones. There is a rapidly growing number of applications of these methods, so it is appropriate to invite students, as well as professionals, to the…

We introduce a technique to decompose the scattered near field of two-dimensional arbitrary metaatoms into its multipole contributions. To this end we expand the scattered field upon plane wave illumination into cylindrical harmonics as…

In theoretical physics, we sometimes have two perturbative expansions of physical quantity around different two points in parameter space. In terms of the two perturbative expansions, we introduce a new type of smooth interpolating function…

Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.

To the best of our knowledge this paper is the first attempt to introduce and study polynomial interpolation of the polynomial data given on arbitrary varieties. In the first part of the paper we present results on the solvability of such…

Theory interpolation has found several successful applications in model checking. We present a novel method for computing interpolants for ground formulas in the theory of equality. The method produces interpolants from colored congruence…

We present the real interpolation with variable exponent and we prove the basic properties in analogy to the classical real interpolation. More precisely, we prove that under some additional conditions, this method can be reduced to the…

The properties of an electron in a typical solid are modified by the interaction with the crystal ions, leading to the formation of a quasiparticle: the polaron. Such polarons are often described using the Fr\"ohlich Hamiltonian, which…

In this paper we prove some interpolation theorems for the multipliers of the Cauchy- Stiltjes type integrals