Distributions, briefly
We’re learning about distributions in the Harmonic Analysis class; these are basically generalized functions. Technically, there are three different types of distributions, each of which is a continuous linear functional from a space of test functions. A distribution is such a functional on the test space 
, a tempered distribution is a functional on the test space 
(the Schwartz space, consisting of 
functions whose derivatives of all orders decay faster than any polynomial), and a distribution with compact support is defined on the test space 
.