Skip to main content
SpringerLink
Log in

Pseudo differential operators with variable order of differentiation generating feller semigroups

  • Published:
Integral Equations and Operator Theory 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.

References

  1. Beauzamy, B.: Espaces de Sobolev et de Besov d'ordre variable définis sur Lp. C. R. Acad. Sci. Paris 274 (1972) 1935–1938.

    Google Scholar 

  2. Berg, C., and Forst, G.: Potential theory on locally compact Abelian groups. Ergebnisse der Mathematik und ihrer Grenzgebiete, II. Ser. Bd. 87, Springer Verlag, Berlin-Heidelberg-New York, (1975).

    Google Scholar 

  3. Bourdaud, G.: Lp-estimates for certain non-regular pseudo-differential operators. Commun. Partial Differential Equations 7 (1982) 1023–1033.

    Google Scholar 

  4. Courrège, Ph.: Sur la forme intégro-différentielle des opérateurs de C ∞K dans C satisfaisant du principe du maximum. Sém. Théorie du Potentiel (1965/66) 38 p.

  5. Illner, R.: A class of Lp-bounded pseudodifferential operators. Proc. Amer. Math. Soc. 51 (1975) 347–355.

    Google Scholar 

  6. Jacob, N.: Feller semigroups, Dirichlet forms, and pseudo differential operators. Forum Math. 4 (1992) 433–446.

    Google Scholar 

  7. Jacob, N.: A class of elliptic pseudo differential operators generating symmetric Dirichlet forms. Potential Analysis 1 (1992) 221–232.

    Google Scholar 

  8. Jacob, N.: Further pseudo differential operators generating Feller semigroups and Dirichlet forms. Rev. Mat. Iberoamericana. (in press)

  9. Jacob, N.: A class of Feller semigroups generated by pseudo differential operators. Math. Z. (to appear)

  10. Kumano-go, H.: Pseudo-differential operators. M.I.T. Press, Cambridge, Massachusetts,-London, (1981).

    Google Scholar 

  11. Leopold, H.-G.: Pseudodifferentialoperatoren und Funktionenräume variabler Glattheit. Dissertation B. Jena: Friedrich-Schiller-Universität, (1987).

    Google Scholar 

  12. Leopold, H.-G.: On Besov spaces of variable order of differentiation. Z. Anal. Anwendungen 8 (1989) 69–82.

    Google Scholar 

  13. Leopold, H.-G.: On function spaces of variable order of differentiation. Forum Math. 3 (1991) 69–82.

    Google Scholar 

  14. Nagase, M.: On the boundedness of pseudo-differential operators in Lp-spaces. Sci. Rep. Coll. Ed. Osaka Univ. 32 (1983) 9–13.

    Google Scholar 

  15. Taylor, M.: Pseudodifferential operators. Princeton Math. Ser., Vol. 34, Princeton University Press, Princeton, New Jersey, (1981).

    Google Scholar 

  16. Triebel, H.: Interpolation theory, function spaces, differential operators. North Holland Mathematical Library Vol. 18, North-Holland Publishing Company, Amsterdam-New York-Oxford, (1978).

    Google Scholar 

  17. Unterberger, A., and Bokobza, J.: Les opérateurs pseudodifférentiels d'ordre variable. C.R. Acad. Sci. Paris 261 (1965) 2271–2273.

    Google Scholar 

  18. Visik, M.I., and Eskin, G.I.: Elliptic convolution equations in a bounded region and their applications. Uspeki Mat. Nauk 22.1 (1967) 15–76. (Russian)

    Google Scholar 

  19. Visik, M.I., and Eskin, G.I.: Convolution equations of variable order. Trudy Moskov. Mat. Obsc. 16 (1967) 26–49 (Russian)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstraße 1a, D-91054, Erlangen, Deutschland

    Niels Jacob

  2. Mathematische Fakultät, Friedrich-Schiller-Universität, Universitätshochhaus 17.OG, D-07743, Jena, Deutschland

    Hans-Gerd Leopold

Authors
  1. Niels Jacob
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hans-Gerd Leopold
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

supported by DFG-contract Ja 522/3-1

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jacob, N., Leopold, HG. Pseudo differential operators with variable order of differentiation generating feller semigroups. Integr equ oper theory 17, 544–553 (1993). https://doi.org/10.1007/BF01200393

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01200393

AMS-Classification

Search

Navigation