Schwartz kernel theorem

In mathematics, the Schwartz kernel theorem is a foundational result in the theory of generalized functions, published by Laurent Schwartz in 1952. It states, in broad terms, that the generalized functions introduced by Schwartz (Schwartz distributions) have a two-variable theory that includes all reasonable bilinear forms on the space ${\displaystyle {\mathcal {D}}}$ of test functions. The space ${\displaystyle {\mathcal {D}}}$ itself consists of smooth functions of compact support.