938 citations · 1.2k across the 21 of their papers we have counts for
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On the volume of unit balls of finite-dimensional Lorentz spaces
Anna Doležalová, Jan Vybíral
We study the volume of unit balls of finite-dimensional Lorentz sequence spaces We give an iterative formula for for the weak Leb…
Entropy numbers of embeddings of Schatten classes
Aicke Hinrichs, Joscha Prochno, Jan Vybiral
Let and denote by and the corresponding finite-dimensional Schatten classes. We prove optimal bounds, up to constants only dep…
Random Matrices and Matrix Completion
Jan Vybiral
The aim of this note (as well as of the course itself) is to give a largely self-contained proof of two of the main results in the field of low-rank matrix recovery. This field aim…
Carl's inequality for quasi-Banach spaces
Aicke Hinrichs, Anton Kolleck, Jan Vybiral
We prove that for any two quasi-Banach spaces and and any there exists a constant such that $$ \sup_{1\le k\le n}k^αe_k(T)\le γ_α\sup_{1\le k\le n} k^αc_k(T)…
On some aspects of approximation of ridge functions
Anton Kolleck, Jan Vybiral
We present effective algorithms for uniform approximation of multivariate functions satisfying some prescribed inner structure. We extend in several directions the analysis of reco…
The Characterization of Radial Subspaces of Besov- and Lizorkin-Triebel Spaces by Differences
Winfried Sickel, Leszek Skrzypczak, Jan Vybiral
We continue our earlier investigations of radial subspaces of Besov and Lizorkin-Triebel spaces on . This time we study characterizations of these subspaces by differences.
Complex Interpolation of Weighted Besov- and Lizorkin-Triebel Spaces (long version)
Winfried Sickel, Leszek Skrzypczak, Jan Vybiral
We study complex interpolation of weighted Besov and Lizorkin-Triebel spaces. The used weights are local Muckenhoupt weights in the sense of Rychkov. As a first step we c…
Spaces of variable smoothness and integrability: Characterizations by local means and ball means of differences
Henning Kempka, Jan Vybiral
We study the spaces of Besov and Triebel-Lizorkin type with variable smoothness and integrability as introduced recently by Almeida & Hästö and Diening, Hästö & Roudenko. Both scal…
A note on the spaces of variable integrability and summability of Almeida and Hästö
Henning Kempka, Jan Vybiral
We address an open problem posed recently by Almeida and Hästö in \cite{AlHa10}. They defined the spaces $\ellqp$ of variable integrability and summability and showed that $\|\cdot…
Average best -term approximation
Jan Vybíral
We introduce the concept of average best -term approximation widths with respect to a probability measure on the unit ball of . We estimate these quantities for the em…
Johnson-Lindenstrauss lemma for circulant matrices
Aicke Hinrichs, Jan Vybíral
We prove a variant of a Johnson-Lindenstrauss lemma for matrices with circulant structure. This approach allows to minimise the randomness used, is easy to implement and provides g…