Approximation of sobolev-type classes with quasi-seminorms

Z. Ditzian, V. N. Konovalov, D. Leviatan

Research output: Contribution to journalArticlepeer-review

Abstract

Since the Sobolev set Wrp, 0 < p < 1, in general is not contained in Lq, 0 < q ≤ ∞, we limit ourselves to the set Wrp ⋂ L 0 < p < 1. We prove that the Kolmogorov n-width of the latter set in Lq, 0 < q < 1 is asymptotically 1, that is, the set cannot be approximated by n-dimensional linear manifolds in the Lq-norm. We then describe a related set, the width of which is asymptotically n.r.

Original languageEnglish
Pages (from-to)445-478
Number of pages34
JournalRocky Mountain Journal of Mathematics
Volume35
Issue number2
DOIs
StatePublished - 2005

Keywords

  • 0 < q < 1
  • N-widths in Lq
  • Sobolev type classes

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