We present several results associated to a holomorphic-interpolation problem for the spectral unit ball Ωn, n ≥ 2. We begin by showing that a known necessary condition for the existence of a O(D; Ωn)-interpolant (D here being the unit disc in C), given that the matricial data are non-derogatory, is not sufficient. We provide next a new necessary condition for the solvability of the two-point in...

Considering a certain interpolation problem, we derive a series of elliptic difference isomonodromic systems together with their Lax forms. These systems give a multivariate extension of the elliptic Painlevé equation.

We prove complex interpolation theorems for analytic families of multilinear operators defined on quasi-Banach spaces, with explicit constants on the intermediate spaces. We obtain analogous results for analytic families of operators defined on spaces generated by the Calderón method applied to couples of quasi-Banach lattices with nontrivial lattice convexity. As an application we derive a mul...

The Cascade-Correlation architecture which is designed for classification tasks has been studied to see if it can be modified to perform function evaluation and interpolation tasks.

Carleson's proof of this theorem involves a difficult covering argument and the consideration of a certain quadratic form (see also [ l ] ) . L. Hörmander later found a proof which appeals to the Marcinkiewicz interpolation theorem and avoids any discussion of quadratic forms. The main difficulty in this approach is to show that a certain sublinear operator is of weak type (1, 1). Here a coveri...

Interpolation technique in color image demosaicing is a big challenge to obtain RGB channels as perceived by humans. The existing demosaicing methods adopt i terative residual interpolation (IRI) technique, which performs iterations on the residuals. These methods are unable to reconstruct G channel efficiently with less iterations. Hence a new demosaicing method is proposed, which performs les...