ABSTRACT
In Chapter 1, we emphasized the distinction between conventional functions and generalized functions. By a conventional function, we mean a function whose domain is a subset of https://www.w3.org/1998/Math/MathML"> R n C n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780138752859/46b98bf4-f43d-4c1b-bad9-d831e2ef6414/content/eq1374.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and whose range is an arbitrary set, but for all practical purposes it is usually taken as a subset of https://www.w3.org/1998/Math/MathML"> R m https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780138752859/46b98bf4-f43d-4c1b-bad9-d831e2ef6414/content/eq1375.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> or https://www.w3.org/1998/Math/MathML"> C m https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780138752859/46b98bf4-f43d-4c1b-bad9-d831e2ef6414/content/eq1376.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . Generalized functions, on the other hand, are not functions in the classical sense, but rather they are mathematical objects. The nature of these objects depends on the approach one uses to construct them.
