We investigate the construction of local quasi-interpolation schemes for a family of bivariate spline functions with smoothness r ≥ 1 and polynomial degree 3r−1. These splines are defined on triangulations with Powell-Sabin refinement, and they can be represented in terms of locally supported basis functions which form a convex partition of unity. Using the blossoming technique, we first derive...

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...

Maxwell equations are posed as variational boundary value problems in the function space H(curl) and are discretized by Nédélec finite elements. In Beck et al., 2000, a residual type a posteriori error estimator was proposed and analyzed under certain conditions onto the domain. In the present paper, we prove the reliability of that error estimator on Lipschitz domains. The key is to establish ...

The application of Orthogonal Space-Time Block Codes (O-STBC) as the encoding scheme in the presence of “non-quasi-static” fading was considered. A simple and efficient adaptive method of channel estimation based on the interpolation of estimates acquired at the pre-amble and post-amble of framed blocks of information is developed. Moreover, the proposed method is proven, both theoretically and...

The basic higher order commutator theorem is formulated for the real interpolation methods associated with the quasi-power parameters, that is, the function spaces on which Hardy inequalities are valid. This theorem unifies and extends various results given by Cwikel, Jawerth, Milman, Rochberg, and others, and incorporates some results of Kalton to the context of commutator estimates for the re...