In this paper, norm estimates are obtained for the problem of minimal-norm tangential interpolation by vector-valued analytic functions in weighted H spaces, expressed in terms of the Carleson constants of related scalar measures. Applications are given to the notion of p-controllability properties of linear semigroup systems and controllability by functions in certain Sobolev spaces.

This paper discusses necessary and sufficient conditions on a monoid S, such that a class D of left S-acts is first order axiomatisable. Such questions have previousely been considered by Bulman-Fleming, Gould, Stepanova and others. Let C be a class of embeddings of right S-acts. A left S-act B is C-flat if tensoring with any B ∈ D preserves the embeddings in C. We find one or two (depending on...

Let R be a finite region of the s-plane and let L2(R) denote the class of functions f(z) each analytic in R with //b|/(8)| 2dS< °°. Let the points ßi, ß2, ß3, • • • be given interior to R and let 0„(z) be that function of class L2(R) for which n(ßi) =n(ß2) = • • • =n(ßn-i) =0, n(ßn) = 1, and which minimizes ffs\ <¡>n(z) \ 2dS over the class L2(R). If the points ßi, ß2, ß3, ■ ■ ■ are...

We prove that W 1 p is a real interpolation space between W 1 p1 and W 1 p2 for p > q0 and 1 ≤ p1 < p < p2 ≤ ∞ on some classes of manifolds and general metric spaces, where q0 depends on our hypotheses.

We consider the biharmonic Dirichlet problem on a polygonal domain. Regularity estimates in terms of Sobolev norms of fractional order are proved. The analysis is based on new interpolation results which generalizes Kellogg’s method for solving subspace interpolation problems. The Fourier transform and the construction of extension operators to Sobolev spaces on R are used in the proof of the i...

derivations, equational logic and interpolation (extended abstract) Gerard R. Renardel de Lavalette Department of Mathematics and Computing Science University of Groningen, the Netherlands Abstract. We define abstract derivations for equational logic and use them to prove the interpolation property. We define abstract derivations for equational logic and use them to prove the interpolation prop...