Abstract
This chapter has a twofold 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 tool in obtaining the solution of the generalized Cauchy problem for the heat operator.
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First considered in 1809 for \(n=1\) by Laplace (cf. [42]) and then for higher dimensions by Poisson (cf. [62] for \(n=2\)).
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Mitrea, D. (2018). The Heat Operator and Related Versions. In: Distributions, Partial Differential Equations, and Harmonic Analysis. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-030-03296-8_8
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DOI: https://doi.org/10.1007/978-3-030-03296-8_8
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