Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Spherical means and radiation conditions

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


  1. [1]

    Baker, B. B., &E. T. Copson: The Mathematical Theory of Huygens' Principle. 2nd Ed. Oxford 1950.

  2. [2]

    Courant, R., & D. Hilbert: Methoden der Mathematischen Physik, vol. 2. Berlin: Springer 1937.

  3. [3]

    Kline, M.: An Asymptotic Solution of Maxwell's Equations. Comm. on Pure and Appl. Math. 4, 225–262 (1951).

  4. [4]

    Kline, M.: Asymptotic Solution of Linear Hyperbolic Partial Differential Equations. J. Rational Mech. and Anal. 3, 315–342 (1954).

  5. [5]

    Luneburg, R. K.: Asymptotic Development of Steady State Electromagnetic Fields. New York University, Math. Research Group, Research Report EM-14 (1949).

  6. [6]

    Müller, C.: Die Grundzüge einer mathematischen Theorie elektromagnetischer Schwingungen. Arch. Math. 1, 296–302 (1948–1949).

  7. [7]

    Rellich, F.: Über das asymptotische Verhalten der Lösungen von Δu+ku=0 in unendlichen Gebieten. Jber. Deutsch. Math. Verein. 53, 57–64 (1943).

  8. [8]

    Silver, S, (Ed.): Microwave Antenna Theory and Design. M.I.T. Radiation Laboratory Series, vol. 12. New York: McGraw-Hill 1949.

  9. [9]

    Sommerfeld, A.: Die Greensche Funktion der Schwingungsgleichung. Jber. Deutsch. Math. Verein. 21, 309–353 (1912).

  10. [10]

    Sommerfeld, A.: Partial Differential Equations in Physics. New York: Academic Press 1949.

  11. [11]

    Stoker, J. J.: Some remarks on radiation conditions, in Proc. of Symposia in Appl. Math., vol. 5, Wave Motion and Vibration Theory, 97–102. New York: McGraw-Hill 1954.

  12. [12]

    Stoker, J. J.: Water Waves. New York: Interscience Publishers 1957.

  13. [13]

    Webster, A. G.: Partial Differential Equations of Mathematical Physics, 2nd Ed., republished by Dover Publications, New York 1955.

  14. [14]

    Wilcox, C. H.: A Generalization of Theorems of Rellich and Atkinson. Proc. A.M.S. 7, 271–276 (1956).

  15. [15]

    Wilcox, C. H.: An Expansion Theorem for Electromagnetic Fields. Comm. on Pure and Appl. Math. 9, 115–134 (1956).

Download references

Author information

Additional information

Communicated by A. Erdélyi

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Wilcox, C.H. Spherical means and radiation conditions. Arch. Rational Mech. Anal. 3, 133–148 (1959).

Download citation


  • Radiation
  • Neural Network
  • Complex System
  • Nonlinear Dynamics
  • Electromagnetism