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Let f be meromorphic on the compact set E ⊂ C with maximal Green domain of meromorphy , ρ(f) < ∞. We investigate rational approximants of f on E with numerator degree ≤ n and denominator degree ≤ mₙ. We show that a geometric convergence rate of order on E implies uniform maximal convergence in m₁-measure inside if mₙ = o(n/log n) as n → ∞. If mₙ = o(n), n → ∞, then maximal convergence in capacity inside can be proved at least for a subsequence Λ ⊂ ℕ. Moreover, an analogue of Walsh’s...
Following the research of Babuška and Práger, the author studies the approximation power of periodic interpolation in the mean square norm thus extending his own former results.
In this paper, we will discuss the meshless polyharmonic reconstruction of vector fields
from scattered data, possibly, contaminated by noise. We give an explicit solution of the
problem. After some theoretical framework, we discuss some numerical aspect arising in the
problems related to the reconstruction of vector fields
In the first section of this paper there are given criteria for strict convexity and smoothness of the Bochner-Orlicz space with the Orlicz norm as well as the Luxemburg norm. In the second one that geometrical properties are applied to the characterization of metric projections and zero mean valued best approximants to Bochner-Orlicz spaces.
Let X be a closed subspace of c₀. We show that the metric projection onto any proximinal subspace of finite codimension in X is Hausdorff metric continuous, which, in particular, implies that it is both lower and upper Hausdorff semicontinuous.
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