Skip to main content
Log in

Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus

Results in Mathematics 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.

Institutional subscriptions

9. References

  1. B. Aulbach, Continuous and Discrete Dynamics near Manifolds of Equilibria. Lecture Notes in Mathematics 1058, Springer, Berlin — Heidelberg —New York — Tokyo, 1984.

    Google Scholar 

  2. G. Boole, A Treatise on the Calculus of Finite Differences, Dover Publications, New York 1960.

    MATH  Google Scholar 

  3. L. Brand, Differential and Difference Equations, Wiley & Sons, New York 1966.

    MATH  Google Scholar 

  4. F.B. Christiansen/ T.M. Fenchel, Theories of Populations in Biological Communities, Springer, Berlin, 1977.

    Book  Google Scholar 

  5. J. Dieudonné, Grundzüge der modernen Analysis Bd. I, Vieweg, Braunschweig 1985.

    Google Scholar 

  6. J. Dieudonné, Grundzüge der modernen Analysis Bd. II, Vieweg, Braunschweig 1987.

    Book  Google Scholar 

  7. M. Erné, Einführung in die Ordnungstheorie. BI-Wissenschaftsverlag, Mannheim, 1982.

    MATH  Google Scholar 

  8. S. Goldberg, Introduction to Difference Equations, Wiley & Sons, New York 1958.

    MATH  Google Scholar 

  9. P. Hartman, Difference Equations: Disconjugacy, Principal Solutions, Green’s Functions, Complete Monotonicity. Trans. AMS 246 (1978), 1–30.

    MathSciNet  MATH  Google Scholar 

  10. S. Hilger, Ein Maβkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten. Dissertation, Univ. Würzburg, 1988.

    Google Scholar 

  11. R.E. Kalman/ J.E. Bertram, Control System Analysis and Design Via the “Second Method of Lyapunov”, I. Continuous Time Systems, II. Discrete Time Systems. Trans. ASME Ser. D, J. of Basic Engineering, 1960, 371 393, 394–400.

    Article  MathSciNet  Google Scholar 

  12. V. Lakshmikantham/ D. Trigiante, Theory of Difference Equations, Academic Press, Inc., San Diego 1988.

    Google Scholar 

  13. J.P. LaSalle, Stability for Difference Equations. In: Studies in Ordinary Differential Equations, MAA Studies in Mathematics 14, Englewood Cliffs, 1977, 1–31.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Work supported by Deutsche Forschungsgemeinschaft, Au 66/3-1

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hilger, S. Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus. Results. Math. 18, 18–56 (1990). https://doi.org/10.1007/BF03323153

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03323153

Keywords

Navigation