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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
First considered in 1809 for \(n=1\) by Laplace (cf. [42]) and then for higher dimensions by Poisson (cf. [62] for \(n=2\)).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-030-03296-8_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-03295-1
Online ISBN: 978-3-030-03296-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)