Skip to main content
Log in

TheC *-algebra of a singular elliptic problem on a noncompact Riemannian manifold

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

References

  1. Breuer, M., Cordes, H. O.: On Banach algebras with σ-symbol. J. Math. Mech.13, 313–324 (1964)

    Google Scholar 

  2. Breuer, M., Cordes, H. O.: On Banach algebras with σ-symbol II. J. Math. Mech.14, 299–314 (1965)

    Google Scholar 

  3. Calderon, A. P., Zygmund, A.: Singular integral operators and differential equations. Amer. J. Math.79, 901–921 (1957)

    Google Scholar 

  4. Carleman, T.: Sur la théorie mathématique de l'équation de Schrödinger. Arkiv for Mat.24, Nr. 11, 7 pp. (1934)

  5. Chernoff, P.: Essential self-adjointness of powers of generators of hyperbolic equations. J. functional Analysis12, 402–414 (1973)

    Google Scholar 

  6. Colella, P., Cordes, H. O.: TheC *-algebra of the elliptic boundary problem. To appear

  7. Cordes, H. O.: Banach algebras and partial differential operators. Lecture notes Lund, 1971

  8. Cordes, H. O.: Beispiele von Pseudo-Differentialoperator-Algebren. Appl. Analysis2, 115–129 (1972)

    Google Scholar 

  9. Cordes, H. O.: Self-adjointness of powers of elliptic operators on non-compact manifolds. Math. Ann.195, 257–272 (1972)

    Google Scholar 

  10. Cordes, H. O.: A global Parametrix for Pseudo-Differential Operators over ℝn, with Applications. SFB 72 Univ. Bonn, No. 90, 1976

  11. Cordes, H. O., Herman, E.: Gel'fand theory of pseudo-differential operators. Amer. J. Math.90, 681–717 (1968)

    Google Scholar 

  12. Cordes, H. O., McOwen, R. C.: Remarks on singular elliptic theory for complete Riemannian manifolds. To appear in Pacific J. Math.

  13. Dixmier, J.: LesC *-algèbras et leurs representations. Paris: Gauthier-Villars 1964

    Google Scholar 

  14. Gaffney, M. P.: The harmonic operator for exterior differential forms. Proc. nat. Acad. Sci. USA37, 48–50 (1951)

    Google Scholar 

  15. Goh'berg, I. C.: On an application of the theory of normed rings to singular integral equations. Uspehi mat. Nauk7, Nr. 2 (48), 149–156 (1952)

    Google Scholar 

  16. Goh'berg, I. C.: On the theory of multi-dimensional singular integral equations. Soviet Math. Doklady1, 960–963 (1960)

    Google Scholar 

  17. Hormander, L.: Pseudo-differential operators and hypoelliptic equations. In: Singular Integrals. Proceedings of Symposia Pure Mathematics. Vol. X (Chicago 1966), pp. 138–183. Providence. American Mathematical Society 1967

    Google Scholar 

  18. Kohn, J.J., Nirenberg, L.: An algebra of pseudo-differential operators. Commun. pure appl. Math.18, 501–517 (1965)

    Google Scholar 

  19. Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry, vol. I. New York-London: Interscience 1963

    Google Scholar 

  20. Kumano-go, H.: Algebras of pseudo-differential operators. J. Fac. Sci., Univ. Tokyo, Sect. I A,17, 31–50 (1970)

    Google Scholar 

  21. Rickart, C. E.: General theory of Banach algebras. Princeton: Van Nostrand 1960

    Google Scholar 

  22. Roelcke, W.: Über den Laplace-Operator auf Riemannschen Mannigfaltigkeiten mit diskontinuierlichen Gruppen. Math. Nachr.21, 132–149 (1960)

    Google Scholar 

  23. Seeley, R. T.: Integro-differential operators on vector bundles. Trans. Amer. math. Soc.117, 167–204 (1965)

    Google Scholar 

  24. Taylor, M. E.: Gel'fand theory of pseudo-differential operators and hypo-elliptic operators. Trans. Amer. math. Soc.153, 495–510 (1971)

    Google Scholar 

  25. Yosida, K.: Functional analysis. Berlin-Heidelberg-New York: Springer 1971

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Both authors were supported in part by an NSF Grant

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cordes, H.O., McOwen, R.C. TheC *-algebra of a singular elliptic problem on a noncompact Riemannian manifold. Math Z 153, 101–116 (1977). https://doi.org/10.1007/BF01179784

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01179784

Keywords

Navigation