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Revista Matemática Complutense

, Volume 29, Issue 1, pp 1–11 | Cite as

Asymptotic formulae for s-numbers of a Sobolev embedding and a Volterra type operator

  • David E. Edmunds
  • Jan LangEmail author
Article

Abstract

Sharp upper and lower estimates are obtained of the approximation numbers of a Sobolev embedding involving second derivatives and an integral operator of Volterra type. These lead to asymptotic formulae for the approximation numbers and certain other s-numbers.

Keywords

Approximation numbers Sobolev embedding Volterra-type operator 

Mathematics Subject Classification

47G10 47B10 

Notes

Acknowledgments

The authors would like to thank Prof. B. Kawohl for information about the literature and Prof. P. Drábek and Prof. J. Benedikt for their valuable comments.

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Copyright information

© Universidad Complutense de Madrid 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SussexBrightonUK
  2. 2.Department of MathematicsOhio State UniversityColumbusUSA

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