Abstract
This chapter has a two fold aim: determine all fundamental solutions that are tempered distributions for the heat operator and related versions (including the Schrödinger operator), then use this as a toll in the solution of the generalized Cauchy problem for the heat operator.
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References
P. S. Laplace, J. École Polytéch. cah., 15 (1809), p. 240 (quoted in Enc. Math. Wiss. Band II, 1. Teil, 2. Hälfte, p. 1198).
S. D. Poisson, Sur l’intégrale de léquation relative aux vibrations des surfaces élastiques et au mouvement des ondes, Bulletin de la Société Philomathique de Paris, (1818), 125–128.
V. S. Vladimirov, Equations of Mathematical Physics, Marcel Dekker Inc., 1971.
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Mitrea, D. (2013). The Heat Operator and Related Versions. In: Distributions, Partial Differential Equations, and Harmonic Analysis. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8208-6_8
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DOI: https://doi.org/10.1007/978-1-4614-8208-6_8
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Print ISBN: 978-1-4614-8207-9
Online ISBN: 978-1-4614-8208-6
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