Abstract
Tempered distributions, as functionals, are continuous with respect to a slightly weaker mode of convergence than that described in Section 2.4, hence are slightly milder, as a class, than the class of all Schwartzian distributions. The mildness is not a local matter (the 03B4 function and all its derivatives are tempered distributions), but has to do with the behavior as ∥x∥ → ∞. The Fourier transform of a tempered distribution is easily defined; it is also a tempered distribution.
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© 1978 Springer-Verlag New York Inc.
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Richtmyer, R.D. (1978). Tempered Distributions and Fourier Transforms. In: Principles of Advanced Mathematical Physics. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46378-5_4
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DOI: https://doi.org/10.1007/978-3-642-46378-5_4
Publisher Name: Springer, Berlin, Heidelberg
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