168 citations · 207 across the 6 of their papers we have counts for
6 papers
The Aubin-Lions-Dubinskii theorems on compactness in Bochner spaces
Harald Hanche-Olsen, Helge Holden
A fundamental issue in the theory of time-dependent differential equations is to characterize precompact sets in Bochner spaces. We here survey the theory, starting with the classi…
On angular measures in axiomatic Euclidean planar geometry
Martin Grötschel, Harald Hanche-Olsen, Helge Holden +1
We address the issue of angular measure, which is a contested issue for the International System of Units (SI). We provide a mathematically rigorous and axiomatic presentation of a…
An improvement of the Kolmogorov-Riesz compactness theorem
Harald Hanche-Olsen, Helge Holden, Eugenia Malinnikova
The purpose of this short note is to provide a new and very short proof of a result by Sudakov, offering an important improvement of the classical result by Kolmogorov-Riesz on com…
Addendum to "The Kolmogorov--Riesz compactness theorem" (Expo. Math. 28:385--394 (2010))
Harald Hanche-Olsen, Helge Holden
We show how to improve on Theorem 10 in [arXiv:0906.4883], describing when subsets in are totally bounded subsets of for and $p\le…
The Kolmogorov-Riesz compactness theorem
Harald Hanche-Olsen, Helge Holden
We show that the Arzela-Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly's theorem…
On the uniform convexity of L^p
Harald Hanche-Olsen
We present a short, direct proof of the uniform convexity of L^p spaces for 1<p<\infty.