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p-spaces

  • Hans TriebelEmail author
Chapter
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

The main aim of Chapter II is to study entropy numbers in (weighted) p -spaces. This will be done in the Sections 7–9. In the present section we describe briefly the necessary abstract background without proofs. We follow closely [ET96] where proofs, further details, explanations, and more references are given.

Keywords

Banach Space Compact Operator Interpolation Property Algebraic Multiplicity Diagonal Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [ET96]
    Edmunds, D.E. and Triebel, H., Function spaces, entropy numbers, differential operators. Cambridge Univ. Press 1996Google Scholar
  2. [HaT94a]
    Haroske, D. and Triebel, H., Entropy numbers in weighted function spaces and eigenvalue distributions of some degenerate pseudodifferential operators I. Math. Nachr. 167 (1994), 131–156zbMATHCrossRefMathSciNetGoogle Scholar
  3. [Pie80]
    Pietsch, A., Operator ideals. Amsterdam, North-Holland, 1980zbMATHGoogle Scholar
  4. [CaS90]
    Carl, B. and Stephani, I., Entropy, compactness and approximation of operators. Cambridge Univ. Press, 1990Google Scholar
  5. [Pie87]
    Pietsch, A., Eigenvalues and s-numbers. Cambridge Univ. Press, 1987Google Scholar
  6. [Carl81]
    Carl, B., Entropy numbers, s-numbers and eigenvalue problems. J. Funct. Analysis 41 (1981), .290–306zbMATHCrossRefMathSciNetGoogle Scholar
  7. [DeVL93]
    DeVore, R.A. and Lorentz, G.G., Constructive approximation. Berlin, Springer, 1993zbMATHGoogle Scholar
  8. [EEv87]
    Edmunds, D.E. and Evans, W.D., Spectral theory and differential operators. Oxford Univ. Press, 1987Google Scholar
  9. [CaT80]
    Carl, B. and Triebel, H., Inequalities between eigenvalues, entropy numbers, and related quantities of compact operators in Banach spaces. Math. Ann. 251 (1980), 129–133zbMATHCrossRefMathSciNetGoogle Scholar
  10. [Tri78]
    Triebel, H., Interpolation theory, function spaces, differential operators. Amsterdam, North-Holland, 1978 (Sec. ed. Heidelberg, Barth, 1995)Google Scholar
  11. [LGM96]
    Lorentz, G.G., Golitschek, M.v. and Makovoz, Y., Constructive approximation, advanced problems. Berlin, Springer, 1996zbMATHGoogle Scholar

Copyright information

© Birkhäuser Verlag 1997

Authors and Affiliations

  1. 1.Mathematisches InstitutFriedrich-Schiller-Universität JenaJenaGermany

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