International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2010). Vol. B, ch. 1.3, p. 32   | 1 | 2 |

## Section 1.3.2.3.9.2. Integration of distributions in dimension 1

G. Bricognea

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#### 1.3.2.3.9.2. Integration of distributions in dimension 1

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The reverse operation from differentiation, namely calculating the indefinite integral' of a distribution S, consists in finding a distribution T such that .

For all such that with , we must haveThis condition defines T in a hyperplane' of , whose equationreflects the fact that ψ has compact support.

To specify T in the whole of , it suffices to specify the value of where is such that : then any may be written uniquely aswithand T is defined byThe freedom in the choice of means that T is defined up to an additive constant.