Skip to main content
SpringerLink
Log in

Eigenvalues of integral operators. II

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Avantaggiati, A.: Spaci di Sobolev con peso ed alcune applicazioni. Boll. Unione Mat. Ital.13A, 1–52 (1976)

    Google Scholar 

  2. Bennett, G.: Inclusion mappings betweenl p-spaces. J. Functional Analysis13, 20–27 (1973)

    Google Scholar 

  3. Bergh, J., Löfström, J.: Interpolation spaces. Berlin, Heidelberg, New York: Springer 1976

    Google Scholar 

  4. Birman, M.S., Solomjak, M.Z.: Estimates of singular numbers of integral operators (in Russian). Parts I–III. Vestnik Leningrad Univ. Math.7, 43–53 (1967);13, 21–28 (1967);1, 35–48 (1969)

    Google Scholar 

  5. Birman, M.S., Solomjak, M.Z.: Quantitative analysis in Sobolev imbedding theorems and applications to spectral theory. 10th Math. School, Kiev 1974, and AMS Translations, Ser. 2, Vol. 114, Providence 1980

  6. Birman, M.S., Solomjak, M.Z.: Estimates for the singular numbers of integral operators (in Russian). Uspehi Mat. Nauk32, No. 1, 17–84 (1977)

    Google Scholar 

  7. Birman, M.S., Solomjak, M.Z.: Asymptotics of the spectrum of differential equations (in Russian). Itogi Nauki, Mat. Anal.14, 5–58 (1977)

    Google Scholar 

  8. Carl, B.: Absolut (p, 1)-summierende identische Operatoren vonl u nachl v . Math. Nachr.63, 353–360 (1974)

    Google Scholar 

  9. Ciesielski, Z.: Constructive function theory and spline systems. Studia Math.53, 277–302 (1975)

    Google Scholar 

  10. Ciesielski, Z., Figiel, T.: Spline bases in classical function spaces in compactC ∞-manifolds (preprint)

  11. Cwikel, M.: Weak type estimates for singular values and the number of bound states of Schrödinger operators. Ann. Math.106, 93–102 (1977)

    Google Scholar 

  12. Desplanches, R.:n-ième diamètre d'une classe d'espaces de Sobolev à poids sur une demi-droite. C.R. Acad. Sci. Paris A284, 1377–1380 (1977)

    Google Scholar 

  13. El Kolli, A.:n-ième épaisseur dans les espaces de Sobolev. J. Approximation Theory10, 268–294 (1974)

    Google Scholar 

  14. Johnson, W.B., König, H., Maurey, B., Retherford, J.R.: Eigenvalues ofp-summing andl p -type operators in Banach spaces. J. Functional Analysis32, 353–380 (1979)

    Google Scholar 

  15. König, H.: Operator properties of Sobolev imbeddings over unbounded domains. J. Functional Analysis24, 32–51 (1977)

    Google Scholar 

  16. König, H.: Interpolation of operator ideals with an application to eigenvalue distribution problems. Math. Ann.233, 35–48 (1978)

    Google Scholar 

  17. König, H.: Some remarks on weakly singular integral operators. Integral Equations Operator Theory3, 397–407 (1980)

    Google Scholar 

  18. König, H.: On the eigenvalue spectrum of certain operator ideals. Colloq. Math.44, 1–28 (1981)

    Google Scholar 

  19. König, H., Retherford, J.R., Tomczak-Jaegermann, N.: On the eigenvalues of (p, 2)-summing operators and constants associated to normed spaces. J. Functional Analysis37, 88–126 (1980)

    Google Scholar 

  20. Kondrashov, V.I.: Sur certaines évaluations pour les familles de fonctions vérifiantes quelques inéqualites integrals. Dokl. Akad. Nauk SSSR18, 235–240 (1938)

    Google Scholar 

  21. Kostometov, G.P., Solomjak, M.Z.: Estimates of the singular numbers of integral operators with a weak singularity (in Russian). Vestnik Leningrad Univ. Math.4, 28–38 (1971)

    Google Scholar 

  22. Kostometov, G.P.: Asymptotic behaviour of the spectrum of integral operators with a singularity on the diagonal (in Russian). Mat. Sbornik94, 444–451 (1974)

    Google Scholar 

  23. Kudrjavcev, L.D.: Imbedding theorems for a class of functions defined on the entire space or a halfspace (in Russian). Parts I and II. Mat. Sbornik69, 616–639 (1966);70, 3–35 (1967)

    Google Scholar 

  24. Kufner, A.: Weighted Sobolev spaces. Teubner Texte Math. Vol. 31. Leipzig: Teubner 1981

    Google Scholar 

  25. Langemann, B.: Über Greensche Funktionen singulärer elliptischer Differentialoperatoren. Studia Math.45, 241–255 (1973)

    Google Scholar 

  26. Lizorkin, P.S., Otelbaev, M.: Imbedding theorems and compactness for spaces of Sobolev type with weights. Parts I and II. Mat. Sbornik108, 358–377 (1979);112, 56–85 (1980)

    Google Scholar 

  27. Métivier, G.: Comportement asymptotique des valeurs propres d'opérateurs elliptiques dégénérés. Soc. Math. France, Astérisque34–35, 215–249 (1976)

    Google Scholar 

  28. Mohamed, A., Pham The Lai: Remarques sur lesn-ièmes diametres d'une classe d'espace de Sobolev a poids. Séminaire de Rennes 1977

  29. Otelbaev, M.: Two-sided estimates of widths and their applications (in Russian). Dokl. Akad. Nauk SSSR231, 810–813 (1976); Soviet Math. Dokl.17, 1655–1659 (1976)

    Google Scholar 

  30. Otelbaev, M.: Estimates of the diameters in the sense of Kolmogoroff for a class of weighted spaces (in Russian). Dokl. Akad. Nauk SSSR235, 1270–1273 (1977); Soviet Math. Dokl.18, 1159–1163 (1977)

    Google Scholar 

  31. Pietsch, A.: Operator ideals. Berlin: Dt. Verlag Wiss. 1978; Amsterdam, New York, Oxford: North-Holland 1980

    Google Scholar 

  32. Pietsch, A.: Über die Verteilung von Fourierkoeffizienten und Eigenwerten. Wiss. Z. FSU Jena, MNR29, 203–211 (1980)

    Google Scholar 

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

    Google Scholar 

  34. Pietsch, A.: Eigenvalues of integral operators. Part I. Math. Ann.247, 169–178 (1980)

    Google Scholar 

  35. Pietsch, A.: Approximation spaces. J. Approximation Theory32, 115–134 (1981)

    Google Scholar 

  36. Ropela, S.: Spline bases in Besov spaces. Bull. Acad. Polon. Sci., Ser. Math. Astr. Phys.24, 319–325 (1976)

    Google Scholar 

  37. Simon, B.: Trace ideals and their applications. London Math. Soc. Lecture Note 35. Cambridge, London, New York, Melbourne: Cambridge Univ. Press 1979

    Google Scholar 

  38. Solomeshch, I.A.: Eigenvalues of some degenerate elliptic equations (in Russian). Mat. Sbornik54, 295–310 (1961)

    Google Scholar 

  39. Solomjak, M.Z.: Estimates of singular numbers of integral operators (in Russian). Part IV. Vestnik Leningrad Univ. Mat.1, 76–87 (1970)

    Google Scholar 

  40. Tamura, H.: The asymptotic eigenvalue distribution for non-smooth elliptic operators. Proc. Jap. Acad.50, 19–22 (1974)

    Google Scholar 

  41. Triebel, H.: Eigenwertverteilungen und Greensche Funktionen entarteter elliptischer Differentialoperatoren. Czech. Math. J.18, 117–136 (1968)

    Google Scholar 

  42. Triebel, H.: Eigenschaften Greenscher Funktionen nichtselbstadjungierter allgemeiner elliptischer Operatoren. Studia Math.30, 339–353 (1968)

    Google Scholar 

  43. Triebel, H.: Über die Verteilung der Approximationszahlen von Integraloperatoren in Sobolev-Besov-Räumen. J. Math. Mech.19, 783–796 (1970)

    Google Scholar 

  44. Triebel, H.: Interpolation theory for function spaces of Besov type defined in domains. Part II. Math. Nachr.58, 63–86 (1973)

    Google Scholar 

  45. Triebel, H.: Spaces of Kudrjavcev type. Parts I and II. Math. Anal. Appl.56, 253–277; 278–287 (1976)

    Google Scholar 

  46. Triebel, H.: Interpolation theory, function spaces, differential operators. Berlin: Dt. Verlag Wiss. 1978; Amsterdam, New York, Oxford: North-Holland 1978

    Google Scholar 

  47. Triebel, H.: Spline bases and spline representation in function spaces. Archiv Math. Basel36, 348–359 (1981)

    Google Scholar 

  48. Weyl, H.: Inequalities between two kinds of eigenvalues of a linear transformation. Acad. Sci. USA35, 408–411 (1949)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sektion Mathematik, Friedrich-Schiller-Universität, DDR-6900, Jena, German Democratic Republic

    Albrecht Pietsch

Authors
  1. Albrecht Pietsch
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pietsch, A. Eigenvalues of integral operators. II. Math. Ann. 262, 343–376 (1983). https://doi.org/10.1007/BF01456014

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01456014

Keywords

Search

Navigation