Abstract
Here all fundamental solutions that are tempered distributions for the wave operator are determined then used as a toll in the solution of the generalized Cauchy problem for this operator.
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Notes
- 1.
This expression for a fundamental solution for the wave operator when n = 1 was first used by Jean d’Alembert in 1747 in connection with a vibrating string.
- 2.
This expression was first found by Vito Volterra (cf. [73]).
References
V. Voltera, Sur les vibrations des corps élastiques isotropes, Acta Math., 18 (1894), 161–232.
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Mitrea, D. (2013). The Wave Operator. In: Distributions, Partial Differential Equations, and Harmonic Analysis. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8208-6_9
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DOI: https://doi.org/10.1007/978-1-4614-8208-6_9
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