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On a Theorem Of Le Roux

  • J. B. Diaz (a1) and G. S. S. Ludford (a2)

Extract

1. The Theorem of Le Roux. Let U(x, y, α) be any solution of the linear hyperbolic differential equation

1

containing a parameter α. J. Le Roux (5) has shown that the function u(x, y) defined by

2 α0 = const.

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References

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1. Bergmann, S., Zitr Theorie der Funktionen, die eine lineare partielle Differ entialgleichung befriedigen, Mathematischeskii Sbornik (NewSer.), 2 (1937), 11691198.
2. Darboux, G., Lecons sur la théorie gén rale des surfaces, 2 (2nd e-resized., Paris 1914-15).
3. Diaz, J. B. and Ludford, G. S. S., On two methods of generating solutions of linear partial differential equations by means of definite integrals, Quarterly Appl. Math., 12 (1955), 422–427; C. R. (Paris), 238 (1954), 19631964.
4. Hadamard, J., Lectures on Cauchy's Problem in Linear Partial Differential Equations (New York, 1952).
5. Le Roux, J., Sur les intégrales des équations linéaires aux derivées partielles du second ordre à deux variables indépendantes, Ann. de l'École Norm. Sup. (3), 12 (1895), 227316.
6. Weinstein, A., The generalized radiation problem and the Ruler-Poisson-Darboux equation, Summa Brasiliensis, to appear in 1955.
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On a Theorem Of Le Roux

  • J. B. Diaz (a1) and G. S. S. Ludford (a2)

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