23 citations · 26 across the 6 of their papers we have counts for
12 papers
An explicit counterexample to the Hinrichs--Vybiral conjecture
Jan Vybiral
Conjecture~2 of Hinrichs and Vybíral asserts that every continuous, nonnegative, positive definite function on , normalized by , satisfies $[f(x_j-x_k)]_{j,k=1}^n…
Gelfand numbers of embeddings of Schatten classes
Aicke Hinrichs, Joscha Prochno, Jan Vybíral
Let and denote by and the corresponding Schatten classes of real matrices. We study the Gelfand numbers of natura…
Lower Bounds for the Error of Quadrature Formulas for Hilbert Spaces
Aicke Hinrichs, David Krieg, Erich Novak +1
We prove lower bounds for the worst case error of quadrature formulas that use given sample points $\X_n = \{ x_1, \dots , x_n \}$. We are mainly interested in optimal point sets $…
Entropy numbers of finite-dimensional embeddings
Marta Kossaczká, Jan Vybíral
Entropy numbers and covering numbers of sets and operators are well known geometric notions, which found many applications in various fields of mathematics, statistics, and compute…
Franke-Jawerth embeddings for Besov and Triebel-Lizorkin spaces with variable exponents
Helena F. Gonçalves, Henning Kempka, Jan Vybíral
The classical Jawerth and Franke embeddings $$ F^{s_0}_{p_0,q}({\mathbb R}^n)\hookrightarrow B^{s_1}_{p_1,p_0}({\mathbb R}^n) \quad \mbox{and} \quad B^{s_0}_{p_0,p_1}({\mathbb R}^n…
Volumes of unit balls of mixed sequence spaces
Henning Kempka, Jan Vybíral
The volume of the unit ball of the Lebesgue sequence space is very well known since the times of Dirichlet. We calculate the volume of the unit ball in the mixed norm $\…
Lorentz spaces with variable exponents
Henning Kempka, Jan Vybíral
We introduce Lorentz spaces and with variable exponents. We prove several basic properties of these spaces including embeddings…
On the Interplay of Regularity and Decay in Case of Radial Functions I. Inhomogeneous spaces
Winfried Sickel, Leszek Skrzypczak, Jan Vybiral
We deal with decay and boundedness properties of radial functions belonging to Besov and Lizorkin-Triebel spaces. In detail we investigate the surprising interplay of regularity an…
Non-smooth atomic decompositions, traces on Lipschitz domains, and pointwise multipliers in function spaces
Cornelia Schneider, Jan Vybíral
We provide non-smooth atomic decompositions for Besov spaces $\Bd(\rn)$, , , defined via differences. The results are used to compute the trace of Besov spac…
Homogeneity property of Besov and Triebel-Lizorkin spaces
Cornelia Schneider, Jan Vybíral
We consider the classical Besov and Triebel-Lizorkin spaces defined via differences and prove a homogeneity property for functions with bounded support in the frame of these spaces…
A variant of the Johnson-Lindenstrauss lemma for circulant matrices
Jan Vybíral
We continue our study of the Johnson-Lindenstrauss lemma and its connection to circulant matrices started in \cite{HV}. We reduce the bound on from proven…
On sharp embeddings of Besov and Triebel-Lizorkin spaces in the subcritical case
Jan Vybíral
We discuss the growth envelopes of Fourier-analytically defined Besov and Triebel-Lizorkin spaces and for . These res…