Skip to main content

The method of transmutations

Part of the Lecture Notes in Mathematics book series (LNM,volume 446)

Keywords

  • Abstract Cauchy Problem
  • Goursat Problem
  • Random Evolution
  • Darboux Equation
  • Dimensional Wave Equation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. COURANT, R. and HILBERT, D., Methods of Mathematical Physics, Vol. II, Wiley (Interscience), New York, 1962.

    MATH  Google Scholar 

  2. LIONS, J. L., Operateurs de Delsarte et problemes mixtes, Bull. Soc. Math. France, 81 (1956), 9–95.

    MathSciNet  MATH  Google Scholar 

  3. LIONS, J. L., On the generalized radiation problem of Weinstein, J. of Math. and Mech. 8 (1959), 873–888.

    MathSciNet  MATH  Google Scholar 

  4. ROTH, W. J., Goursat problems for urs=Lu, Indiana Univ. Math. J. 22 (1973), 779–788.

    CrossRef  MATH  Google Scholar 

  5. BALAKRISHNAN, A. V., Abstract Cauchy problems of the elliptic type, Bull. Amer. Math. Soc. 64 (1958), 290–291.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. BRAGG, L. R. and DETTMAN, J. W., Related problems in partial differential equations, Bull. Amer. Soc. 74 (1968), 375–378.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. GRIEGO, R. and HERSH, R., Theory of random evolutions with applications to partial differential equations, Trans. Amer. Math. Soc. 156 (1971), 405–418.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. ROMANOV, N. P., On one-parmeter groups of linear transformation, I, Ann. of Math. (2) 48 (1947), 216–233.

    CrossRef  Google Scholar 

  9. UNGAR, A., On an integral transform related to the wave and to the heat equations, A. M. S. Notices 18 (1971), 1100.

    Google Scholar 

  10. HERSH, R., Explicit solution of a class of higher-order abstract Cauchy problems, J. of Differential Equations 8 (1970), 570–579.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. TRANTER, C. J., Bessel Functions with some Physical Applications, The English Universities Press Ltd., London, 1968.

    MATH  Google Scholar 

  12. DONALDSON, J. A., An operational calculus for a class of abstract operator equations, J. of Math. Anal. and Appl. 37 (1972), 167–184.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. KAC, M., Some stochastic problems in physics and mathematics, Magnolia Petroleum Co. Colloquium Lectures, 2 (1956); reprinted in Rocky Mt. Math. J., Summer, 1974.

    Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. ROSENCRANS, S. I., Diffusion transforms, J. of Differential Equations 13 (1973), 457–467.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. BOBISUD, L. and HERSH, R., Perturbation and approximation theory for higher-order abstract Cauchy problems, Rocky Mt. J. of Math. 2 (1972), 57–73.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. DONALDSON, J. A., A singular Cauchy problem with a small parameter, Howard University Preprint.

    Google Scholar 

  18. HERSH, R., Stochastic solutions of hyperbolic equations, this volume.

    Google Scholar 

  19. BRAGG, L. R. and DETTMAN, J. W., An operator calculus for related partial differential equations, J. of Math. Anal. and Appl. 22 (1968), 261–271.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. BRAGG, L. R., Hypergeometric operator series and related partial differential equations, Trans. Amer. Math. Soc. 143 (1969), 319–336.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. DETTMAN, J. W., Initial-boundary value problems related through the Stieltjes transform, J. of Math. Anal. and Appl. 25 (1969), 341–349.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1975 Springer-Verlag

About this paper

Cite this paper

Hersh, R. (1975). The method of transmutations. In: Goldstein, J.A. (eds) Partial Differential Equations and Related Topics. Lecture Notes in Mathematics, vol 446. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0070606

Download citation

  • DOI: https://doi.org/10.1007/BFb0070606

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07148-8

  • Online ISBN: 978-3-540-37440-4

  • eBook Packages: Springer Book Archive