On the boundedness of the mapping in Besov spaces
For , precise conditions on the parameters are given under which the particular superposition operator is a bounded map in the Besov space . The proofs rely on linear spline approximation theory.
On the control net of certain multivariate spline functions
On the Degree of Approximation by Spline Functions with Free Knots.
On the Dimension of Bivariate Spline Spaces of Smoothness r and Degree d = 3r + 1.
On the exact estimates of the best spline approximations of functions.
On the Fejér means of bounded Ciesielski systems
We investigate the bounded Ciesielski systems, which can be obtained from the spline systems of order (m,k) in the same way as the Walsh system arises from the Haar system. It is shown that the maximal operator of the Fejér means of the Ciesielski-Fourier series is bounded from the Hardy space to if 1/2 < p < ∞ and m ≥ 0, |k| ≤ m + 1. Moreover, it is of weak type (1,1). As a consequence, the Fejér means of the Ciesielski-Fourier series of a function f converges to f a.e. if f ∈ L₁ as n...
On the local linear independence of translates of a box spline
On the total positivity of the truncated power kernel
On the two dimensional spline interpolation of Hermite-type.
Operator norm bounds and error bounds for quadratic spline interpolation
Optimal discrete approximation of continuous linear operators applicable to control problems
Optimal interpolatory splines using -spline representation
Optimal polygonal interpolation
Optimal quadratic interpolatory splines on general knotset
Optimal Rules with Polynomial Precision for Hilbert Spaces Possessing Reproducing Kernel Functions.
Oscillation Matrices with Spline Smoothing.