5 papers
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…
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 $\…
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…