We obtain a result concerning the stability under the interpolation with functional parameter method for the approximation spaces of LorentzMarcinkiewicz type and also for the approximation spaces generated by symmetric norming functions of a certain type.

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We prove optimal order error estimates for the Raviart-Thomas interpolation of arbitrary order under the maximum angle condition for triangles and under two generalizations of this condition, namely, the so-called three dimensional maximum angle condition and the regular vertex property, for tetrahedra. Our techniques are different from those used in previous papers on the subject and the resul...

We prove a general result on the factorization of matrix-valued analytic functions. We deduce that if (E0, E1) and (F0, F1) are interpolation pairs with dense intersections, then under some conditions on the spaces E0, E1, F0 and F1, we have [E0⊗̂F0, E1⊗̂F1]θ = [E0, E1]θ⊗̂[F0, F1]θ, 0 < θ < 1. We find also conditions on the spaces E0, E1, F0 and F1 , so that the following holds [E0 ∨ ⊗F0, E1 ∨ ⊗F1...

It is known that every dimension group with order-unit of size at most א1 is isomorphic to K0(R) for some locally matricial ring R (in particular, R is von Neumann regular); similarly, every conical refinement monoid with order-unit of size at most א1 is the image of a V-measure in Dobbertin’s sense, the corresponding problems for larger cardinalities being open. We settle these problems here, ...

We prove: if d/m < 2280/721, there is no curve of degree d passing through n = 10 general points with multiplicity m in P. Similar results are given for other special values of n. Our bounds can be naturally written as certain palindromic continued fractions.

The potential beneets of a uniform version of interpolation are hindered by its absence from many expressive logics. This motivates a thorough investigation of appropriate expansions of known entailments so that an easy-to-derive, uniform presentation of the interpolants is supported. This paper presents the skeleton of a general construction and indicates that a potentially large class of enta...

Let α be an infinite cardinal. In this paper we define an interpolation rule IR(α) for lattice ordered groups. We denote by C(α) the class of all lattice ordered groups satisfying IR(α), and prove that C(α) is a radical class.