arXiv subjects

David E Edmunds

Publications and source records attributed to David E Edmunds.

3 recordsLinked to original sources

arXiv2025

Notes on Non-Compact Maps and the Importance of Bernstein Numbers

In this review paper we study non-compact operators and embeddings between function spaces, highlighting interesting phenomena and the significance of Bernstein numbers. In particular, we demonstrate that for non-compact maps the usual $s$-numbers (e.g., approximation, Kolmogorov, and entropy numbers) fail to reveal finer structural properties, and one must instead consider concepts such as strict singularity and Bernstein numbers.

math.FA↗

arXiv2018

Behaviour of $L_{q}$ norms of the $\sinc_{p}$ function

An integral inequality due to Ball involves the $L_{q}$ norm of the $\sinc_p$ function; the dependence of this norm on $q$ as $q\rightarrow\infty$ is now understood. By use of recent inequalities involving $p-$trigonometric functions $(1<p<\infty )$ we obtain asymptotic information about the analogue of Ball's integral when $\sin$ is replaced by $\sin_{p}.$

math.NA↗

arXiv2013

Schutt's theorem for vector-valued sequence spaces

The entropy numbers of certain finite-dimensional operators acting between vector-valued sequence spaces are estimated, thus providing a generalization of the famous result of Schutt. In addition, two-sided estimates of the entropy numbers of some diagonal operators are obtained.

math.SP↗