18 citations · 38 across the 22 of their papers we have counts for
26 papers
Properties of local orthonormal systems, Part III: Variation spaces
Jacek Gulgowski, Anna Kamont, Markus Passenbrunner
In [Y.~K.~Hu, K.~A.~Kopotun, X.~M.~Yu, Constr. Approx. 2000], the authors have obtained a characterization of best -term piecewise polynomial approximation spaces as real interp…
Properties of local orthonormal systems, Part II: Geometric characterization of Bernstein inequalities
Jacek Gulgowski, Anna Kamont, Markus Passenbrunner
Let be a probability space and let be a binary filtration, i.e. exactly one atom of is divided into two atoms of $\m…
Properties of local orthonormal systems, Part I: Unconditionality in
Jacek Gulgowski, Anna Kamont, Markus Passenbrunner
Assume that we are given a filtration on a probability space of the form that each is generated by the partition of one a…
Multivariate orthogonal spline systems
M. Passenbrunner
In this article we consider orthonormal systems consisting of tensor products of splines. We show some convergence results of the corresponding orthogonal series including a.e. con…
An algebraic characterization of B-splines
Anna Kamont, Markus Passenbrunner
B-splines of order can be viewed as a mapping taking a -tuple of increasing real numbers and giving as a result a certain piecewise polynomial f…
Martingale convergence Theorems for Tensor Splines
Markus Passenbrunner
In this article we prove martingale type pointwise convergence theorems pertaining to tensor product splines defined on -dimensional Euclidean space ( is a positive integer),…
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.
Almost everywhere Convergence of Spline Sequences
Paul F. X. Müller, Markus Passenbrunner
We prove the analogue of the Martingale Convergence Theorem for polynomial spline sequences. Given a natural number and a sequence of knots in with multiplicit…
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…
Orthogonal projectors onto spaces of periodic splines
Markus Passenbrunner
The main result of this paper is a proof that for any integrable function on the torus, any sequence of its orthogonal projections onto periodic spline sp…
Estimating averages of order statistics of bivariate functions
Richard Lechner, Markus Passenbrunner, Joscha Prochno
We prove uniform estimates for the expected value of averages of order statistics of bivariate functions in terms of their largest values by a direct analysis. As an application, u…
Uniform Estimates for Averages of Order Statistics of Matrices
Richard Lechner, Markus Passenbrunner, Joscha Prochno
We prove uniform estimates for the expected value of averages of order statistics of matrices in terms of their largest entries. As an application, we obtain similar probabilistic…
Unconditionality of orthogonal spline systems in
Gegham Gevorkyan, Anna Kamont, Karen Keryan +1
We give a simple geometric characterization of knot sequences for which the corresponding orthonormal spline system of arbitrary order is an unconditional basis in the atomic H…
Probabilistic estimates for tensor products of random vectors
David Alonso-Gutierrez, Markus Passenbrunner, Joscha Prochno
We prove some probabilistic estimates for tensor products of random vectors. As an application we obtain embeddings of certain matrix spaces into .
Adaptive deterministic dyadic grids on spaces of homogeneous type
Richard Lechner, Markus Passenbrunner
In the context of spaces of homogeneous type, we develop a method to deterministically construct dyadic grids, specifically adapted to a given combinatorial situation. This method…
On almost everywhere convergence of tensor product spline projections
Markus Passenbrunner, Joscha Prochno
Let and be a function in the Orlicz class defined on the unit cube in . Given partitions of $[0,1…
Unconditionality of orthogonal spline systems in
Markus Passenbrunner
Given any natural number and any dense point sequence , we prove that the corresponding orthonormal spline system of order is an unconditional basis in reflexive $L^…
On the Distribution of Random variables corresponding to Musielak-Orlicz norms
David Alonso-Gutierrez, Soeren Christensen, Markus Passenbrunner +1
Given a normalized Orlicz function we provide an easy formula for a distribution such that, if is a random variable distributed accordingly and are independen…
Pointwise estimates for B-spline Gram matrix inverses
Markus Passenbrunner
We present a new method for proving a certain geometric-decay inequality for entries of inverses of B-spline Gram matrices, which is given in [Passenbrunner,Shadrin 2013, arXiv:130…
Monotonicity of the Lebesgue constant for equally spaced knots
Markus Passenbrunner
Let for be equally spaces knots in the unit interval Let be the space of piecewise linear continuous functions on …