Maximal order for quadratures using n evaluations.
Maximally convergent rational approximants of meromorphic functions
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...
Minimum Relative Error Approximations for 1/t.
Mixed K-Functionals: A Measure of Smoothness for Blending-type Approximation.
Modifizierte Restgliedabschätzungen für Quadraturformeln.
Moment computation in shift invariant spaces.