By the Fricke surfaces, we mean the space defined by the equation p2 + q2 + r2 − pqr− k = 0 in the space R(p, q, r). When k = 0, it is naturally isomorphic to the moduli of once-punctured tori. It was Markoff who found the transformations, called Markoff transformations, acting on the Fricke surface. The transformation is typically given by (p, q, r) → (r, q, rq − p) acting on R3 that keeps the...

After 41 years it is still not known whether an operator acting on a Banach pair and which acts compactly on one or both of the “endpoint” spaces also acts compactly on the complex interpolation spaces generated by the pair. We report some recent steps towards solving this and related problems.

The purpose of this paper is to explain how to compute the function Í2 which interpolates values of a function of one variable fix) at n distinct points x, ik) < x2 < ■ • • < *n_i < x„, and which, whenever ll/v 'H^ is bounded and the value of the bound is unknown, provides the smallest possible value of Bix) in the error bound \fix) Í2(x)l < B(*)ll/(fc)lloo

We consider positive definite (semidefinite) extension problems for matrices with structure determined via a Stein equation. Some related extremal problems (maximal and minimal rank extensions, maximal determinant extension) are also considered. Connections with interpolation problems for a certain class of analytic contractive valued functions on the unit ball of Cd are discussed. © 2003 Publi...

Uniformly sampled images are often used to interpolate other data acquired more sparsely with an entirely different mode of measurement. For example, downhole tools enable geophysical properties to be measured with high precision near boreholes that are scattered spatially, and less precise seismic images acquired at the earth’s surface are used to interpolate those properties at locations far ...

The building façade model is the most prominent streetscape feature for rendering virtual street models. This paper aims to develop a method to identify street obstacles which hinder photo-realistic texturing of building façade. In order to achieve this, the presented method focuses on two research components. Firstly, we develop an effective grid-based line analysis method to differentiate ima...

A bounded linear operator that maps H to L and L to L is bounded from L to L for each p ∈ (1, 2), by a famous interpolation result of Fefferman and Stein. We prove L-norm bounds that grow like O ( 1/(p− 1) ) as p ↓ 1. This growth rate is optimal, and improves significantly on the previously known exponential bound O(21/(p−1)).

We solve a tangential boundary interpolation problem with a finite number of interpolating points for a multivariable analogue of the Schur class. The description of all solutions is parametrized in terms of a linear fractional transformation whose entries are given explicitly in terms of the interpolation data. © 2002 Elsevier Science Inc. All rights reserved. AMS classification: 32A30; 47A56;...

We continue the study of centralizers on Kothe function spaces and the commutator estimates they generate (see [29]). Our main result is that if X is a super-reflexive Kothe function space then for every real centralizer Q on X there is a complex interpolation scale of Kothe function spaces through X inducing Q as a derivative, up to equivalence and a scalar multiple. Thus, in a loose sense, al...