Skip to main content
Log in

Convolution semigroups and generalized telegraph equations

  • 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. Goldstein, S.: On diffusion by discontinuous movements, and on the telegraph equation. Quart. J. Mech. Appl. Math.4, 129–156 (1951)

    Google Scholar 

  2. Gradshteyn, I.S., Ryzhik, I.M.: Table of integrals, series and products. Corrected and enlarged edition. New York-London-Toronto-Sydney-San Francisco: Academic Press 1980

    Google Scholar 

  3. Griego, R., Hersh, R.: Theory of random evolutions with applications to partial differential equations. Trans. Amer. Math. Soc.156, 405–418 (1971)

    Google Scholar 

  4. Hazod, W.: Stetige Faltungshalbgruppen von Wahrscheinlichkeitsmaßen und erzeugende Distributionen. Lecture Notes in Mathematics595. Berlin-Heidelberg-New York: Springer 1977

    Google Scholar 

  5. Hellwig, G.: Partielle Differentialgleichungen. Stuttgart: Teubner 1960

    Google Scholar 

  6. Heyer, H.: Probability measures on locally compact groups. Berlin-Heidelberg-New York: Springer 1977

    Google Scholar 

  7. Hille, E., Phillips, R.S.: Functional analysis and semi-groups. American Methematical Society Colloquium Publications31, revised edition. Providence, Rhode Island: Americian Mathematical Society 1957

    Google Scholar 

  8. Kac, M.: A stochastic model related to the telegrapher's equation. In: Some stochastic problems in physics and mathematics. Magnolia Petroleum Co., Lectures in Pure and Applied Science2, 1956. Reprinted in: Rocky Mountain J. Math.4, 497–509 (1974)

  9. Kaplan, S.: Differential equations in which the Poisson process plays a role. Bull. Amer. Math. Soc.70, 264–268 (1964)

    Google Scholar 

  10. Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966

    Google Scholar 

  11. Kisyński, J.: On M. Kac's probabilistic formula for the solution of the telegraphist's equation. Ann. Polon. Math.29, 259–272 (1974)

    Google Scholar 

  12. Pinsky, M.: Differential equations with a small parameter and the central limit theorem for functions defined on a finite Markov chain. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete9, 101–111 (1968)

    Google Scholar 

  13. Schoene, A.: Semi-groups and a class of singular perturbation problems. Indiana Univ. Math. J.20, 247–263 (1970)

    Google Scholar 

  14. Siebert, E.: Diffuse and discrete convolution semigroups of probability measures on topological groups. Rend. Mat. (to appear)

  15. Taylor, G.I.: Diffusion by continuous movements. Proc. London Math. Soc.20, 196–212 (1992)

    Google Scholar 

  16. Yosida, K.: Functional Analysis. 3rd ed. Berlin-Heidelberg-New York: Springer 1971

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Janssen, A., Siebert, E. Convolution semigroups and generalized telegraph equations. Math Z 177, 519–532 (1981). https://doi.org/10.1007/BF01219084

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01219084

Keywords

Navigation