
Chapter 2 1
Elements of Theory
of Generalized Functions
21.1 Generalized Functions of One Variable
21.1.1 Impor tant Terminologi cal Remark
The main subject of this chapter—generalized functions—has in fact two names in the
literature. One name, “generalized functions,” tends to be more popular among engineers
and physicists; it probably goes back to Dirac and was firmly introduced in practice by
Gelfand and Shilov. The other name, “distributions,” mostly preferred by mathematicians,
stems from the seminal work of Laurent Schwartz. We use both terms interchangeably but
prefer “distributions”—just because it is shorter, one word instead of two.
21.1.2