Skip to main content
SpringerLink
Log in

Differential equations in operator algebras

I. Invariance of the Siegel disk

  • 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.

References

  1. Aumann, G.: Reelle Funktionen. Springer Grundlehren 68, p. 222. 2. Aufl. Berlin-Heidelberg-New York: Springer 1969

    Google Scholar 

  2. Beckenbach, E. F.: Modern mathematics for the engineer, 2. Ser., Chap. 12. New York, Toronto, London: McGraw-Hill 1961

    Google Scholar 

  3. Bellman, R., Wing, G. M.: An introduction to invariant imbedding. New York, London, Sydney, Toronto: Wiley 1975

    Google Scholar 

  4. Chandrasekhar, S.: Radiative transfer. Oxford: University Press 1950

    Google Scholar 

  5. Deimling, K.: Ordinary differential equations in Banach spaces. Lecture Notes in Mathematics 596. Berlin-Heidelberg-New York: Springer 1977

    Google Scholar 

  6. Heuser, H.: Funktionalanalysis. Stuttgart: Teubner 1975

    Google Scholar 

  7. Martin, R. H., Jr: Nonlinear operators and differential equations in Banach spaces. New York, London, Sydney, Toronto: Wiley 1976

    Google Scholar 

  8. Mazur, S.: Über konvexe Mengen in linearen normierten Räumen, Studia Math.4, 70–84 (1933)

    Google Scholar 

  9. Preisendorfer, R.: Invariant imbedding relation for the principles of invariance; functional relations forR andT operators on plane parallel media. Proc. Nat. Acad. Sci., USA, 320–323, 323–328 (1958)

  10. Redheffer, R. M.: Inequalities for a matrix Riccati equation. J. Math. Mech.8, 349–367 (1959). See also, Supplementary Note, ibid.9, 745–748 (1960)

    Google Scholar 

  11. Redheffer, R. M.: On the relation of transmission-line theory to scattering and transfer. J. Math. Phys.41, 1–41 (1962)

    Google Scholar 

  12. Redheffer, R. M.: Matrix differential equations. Bull. Amer. Math. Soc.81, 485–488 (1975)

    Google Scholar 

  13. Redheffer, R. M.: Matrix equations in the Siegel disk, optimal control and differential equations, pp. 277–292. New York, San Francisco, London: Academic Press 1978

    Google Scholar 

  14. Redheffer, R. M., Walter, W.: A differential inequality for the distance function in normed linear spaces. Math. Ann.211, 299–314 (1974)

    Google Scholar 

  15. Reid, W. T.: Solutions of a Riccati matrix differential equation as functions of the initial values, J. Math. Mech.8, 221–230 (1959)

    Google Scholar 

  16. Reid, W. T.: Properties of solutions of a Riccati matrix differential equation. J. Math. Mech.9, 749–770 (1960)

    Google Scholar 

  17. Reid, W. T.: Riccati differential equations. New York, London: Academic Press 1972

    Google Scholar 

  18. Saks, S.: Theory of the integral, p. 203ff (Second revised edition), New York: Dover 1964

    Google Scholar 

  19. Volkmann, P.: Über die Invarianz konvexer Mengen und Differentialungleichungen in normierten Räumen, Math. Ann.203, 201–210 (1973)

    Google Scholar 

  20. Volkmann, P.: Über die Invarianzsätze von Bony und Brézis in normierten Räumen. Arch. Math. (Basel)26, 89–93 (1975)

    Google Scholar 

  21. Zakhar-Itkin, M. Kh.: The matrix Riccati differential equation and the semi-group of linear fractional transformations. Russian Math. Surveys28, 89–131 (1973)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of California at Los Angeles, 90024, Los Angeles, CA, USA

    Ray Redheffer

  2. Mathematisches Institut I der Universität Karlsruhe, D-7500, Karlsruhe, Germany

    Peter Volkmann

Authors
  1. Ray Redheffer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter Volkmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was initiated under auspices of the U.S. Special Program, von Humboldt-Stiftung, and was supported in part by NSF Grant No. MCS 77-03570

Rights and permissions

Reprints and permissions

About this article

Cite this article

Redheffer, R., Volkmann, P. Differential equations in operator algebras. Math. Ann. 239, 97–110 (1979). https://doi.org/10.1007/BF01420367

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01420367

Keywords

Search

Navigation