5 citations · 5 across the 3 of their papers we have counts for
6 papers
Orthoprojectors on perturbations of splines spaces
Karen Keryan, Markus Passenbrunner
We show that -norms of orthoprojectors on certain types of perturbations of spline spaces are bounded independently of the knot sequence. Explicit applications of this re…
Extremal Distributions of Discrepancy functions
Ralph Kritzinger, Markus Passenbrunner
The irregularities of a distribution of points in the unit interval are often measured with various notions of discrepancy. The discrepancy function can be defined with respect…
Martingale inequalities for spline sequences
Markus Passenbrunner
We show that D. Lépingle's -inequality \begin{equation*} \Big\| \big( \sum_n \mathbb E[f_n | \mathscr F_{n-1}]^2 \big)^{1/2}\Big\|_1 \leq 2\cdot \Big\| \big( \sum_n f_…
Projection operators onto spaces of Chebyshev splines
Karen Keryan, Markus Passenbrunner
We prove that the Chebyshev spline orthoprojectors are uniformly bounded on .
Spline Characterizations of the Radon-Nikodým property
Markus Passenbrunner
We give necessary and sufficient conditions for a Banach space having the Radon-Nikodým property in terms of polynomial spline sequences.
Unconditionality of Periodic Orthonormal Spline Systems in
K. Keryan, M. Passenbrunner
Given any natural number and any dense point sequence on the torus , we prove that the corresponding periodic orthonormal spline system of order is an un…