Skip to main content
SpringerLink
Log in
Book cover

Ordinary and Partial Differential Equations pp 213–231Cite as

Entropy numbers, s-numbers and eigenvalues

  • Conference paper
  • First Online:

  • 743 Accesses

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 964))

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. F.E. Browder, On the spectral theory of elliptic differential operators, I, Math. Ann. 142 (1960/61), 22–130.

    Article  MathSciNet  MATH  Google Scholar 

  2. B. Carl, Entropy numbers, entropy moduli, s-numbers and eigenvalues of operators in Banach spaces (preprint).

    Google Scholar 

  3. B. Carl, Entropy numbers of embedding maps between Besov spaces with an application to eigenvalue problems, Proc. Roy. Soc. Edinburgh 90A (1981), 63–70.

    Article  MathSciNet  MATH  Google Scholar 

  4. B. Carl and H. Triebel, Inequalities between eigenvalues, entropy numbers and related quantities of compact operators in Banach spaces, Math. Ann. 251 (1980), 129–133.

    Article  MathSciNet  MATH  Google Scholar 

  5. D.E. Edmunds and W.D. Evans, Elliptic and degenerate elliptic operators in unbounded domains, Ann. Scuola Norm. Sup. Pisa 27 (1973), 591–640.

    MathSciNet  MATH  Google Scholar 

  6. D.E. Edmunds, W.D. Evans and J. Fleckinger, to appear.

    Google Scholar 

  7. D.E. Edmunds and M.F. Teixeira, Interpolation theory and measures of non-compactness, Math. Nachrichten (to appear).

    Google Scholar 

  8. D.E. Edmunds and H. Triebel, Entropy numbers for non-compact self-adjoint operators in Hilbert spaces, Math. Nachrichten 100 (1981), 213–219.

    Article  MathSciNet  MATH  Google Scholar 

  9. W.D. Evans, Semi-bounded Dirichlet integrals and the invariance of the essential spectra of self-adjoint operators, Proc. Roy. Soc. Edinburgh A75 (1975), 41–66.

    Article  MathSciNet  MATH  Google Scholar 

  10. J. Fleckinger, Estimation des valeurs propres d'opérateurs elliptiques sur des ouverts non bornés, Ann. Fac. Sci. Toulouse 12 (1980), 157–180.

    Article  MathSciNet  MATH  Google Scholar 

  11. K. Hayakawa, Interpolation by the real method preserves compactness of operators, J. Math. Soc. Japan 21 (1969), 189–199.

    Article  MathSciNet  MATH  Google Scholar 

  12. T. Kato, Perturbation theory for linear operators (Berlin-Heidelberg-New York: Springer-Verlag, 1966).

    Book  MATH  Google Scholar 

  13. H. König, A formula for the eigenvalues of a compact operator, Studia Math. 65 (1979), 141–146.

    MathSciNet  MATH  Google Scholar 

  14. A. Lebow and M. Schechter, Semigroups of operators and measures of non-compactness, J. Functional Anal. 7 (1971), 1–26.

    Article  MathSciNet  MATH  Google Scholar 

  15. J.-L. Lions and J. Peetre, Sur une classe d'espaces d'interpolation, Inst. Hautes Études Sci. Publ. Math. 19 (1964), 5–68.

    Article  MathSciNet  Google Scholar 

  16. G. Métivier, Valeurs propres de problèmes aux limites elliptiques irréguliers, Bull. Soc. Math. France Mem. 51–52 (1977), 125–219.

    MATH  Google Scholar 

  17. B.S. Mitjagin and A. Pelczýnski, Nuclear operators and approximative dimension, Proc. I.C.M. Moscow (1966), 366–372.

    Google Scholar 

  18. R.D. Nussbaum, The radius of the essential spectrum, Duke Math. J. 38 (1970), 473–478.

    Article  MathSciNet  MATH  Google Scholar 

  19. A. Persson, Compact linear mappings between interpolation spaces, Arkiv Math. 5 (1964), 215–219.

    Article  MathSciNet  MATH  Google Scholar 

  20. A. Pietsch, Operator ideals (Berlin: Verlag der Wissenschaften and North-Holland, 1978/80).

    MATH  Google Scholar 

  21. A. Pietsch, Weyl numbers and eigenvalues of operators in Banach spaces, Math. Ann. 247 (1980), 149–168.

    Article  MathSciNet  MATH  Google Scholar 

  22. C.A. Stuart, Some bifurcation theory for k-set contractions, Proc. Lond. Math. Soc. 27 (1973), 531–550.

    Article  MathSciNet  MATH  Google Scholar 

  23. M.F. Teixeira, Entropy numbers and interpolation, Math. Nachrichten (to appear).

    Google Scholar 

  24. H. Triebel, Interpolationseigenschaften von Entropie-und Durchmesseridealen kompakter Operatoren, Studia Math. 34 (1970), 89–107.

    MathSciNet  MATH  Google Scholar 

  25. H. Triebel, Interpolation theory, function spaces, differential operators (Berlin: Verlag der Wissenschaften and North-Holland, 1978).

    MATH  Google Scholar 

  26. H. Weyl, Inequalities between the two kinds of eigenvalues of a linear transformation, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 408–11.

    Article  MathSciNet  MATH  Google Scholar 

  27. J. Zemanek, The essential radius and the Riesz part of spectrum (1980 preprint).

    Google Scholar 

Download references

Authors
  1. D. E. Edmunds
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

W.N. Everitt B.D. Sleeman

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Edmunds, D.E. (1982). Entropy numbers, s-numbers and eigenvalues. In: Everitt, W., Sleeman, B. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 964. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065000

Download citation

  • DOI: https://doi.org/10.1007/BFb0065000

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11968-5

  • Online ISBN: 978-3-540-39561-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation