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Zeitschrift für Analysis und ihre Anwendungen


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Volume 31, Issue 2, 2012, pp. 161–181
DOI: 10.4171/ZAA/1453

Published online: 2012-03-30

Coincidence and Calculation of some Strict $s$-Numbers

David E. Edmunds[1] and Jan Lang[2]

(1) University of Sussex, Brighton, United Kingdom
(2) Ohio State University, Columbus, USA

The paper considers the so-called strict $s$-numbers, which form an important subclass of the family of all $s$-numbers. For operators acting between Hilbert spaces the various $s$-numbers are known to coincide: here we give examples of linear maps $T$ and non-Hilbert spaces $X, Y$ such that all strict $s$-numbers of $T : X \to Y$ coincide. The maps considered are either simple integral operators acting in Lebesgue spaces or Sobolev embeddings; in these cases the exact value of the strict $s$-numbers is determined.

Keywords: $s$-Numbers, generalized trigonometric functions, Sobolev embedding, Hardy operator, widths, compact maps, asymptotic estimates

Edmunds David, Lang Jan: Coincidence and Calculation of some Strict $s$-Numbers. Z. Anal. Anwend. 31 (2012), 161-181. doi: 10.4171/ZAA/1453