The Titchmarsh convolution theorem describes the properties of the
support
Support may refer to:
Arts, entertainment, and media
* Supporting character
Business and finance
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Construction
* Support (structure), or lateral support, a ...
of the
convolution
In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions ( and ) that produces a third function (f*g) that expresses how the shape of one is modified by the other. The term ''convolution'' ...
of two functions. It was proven by
Edward Charles Titchmarsh
Edward Charles "Ted" Titchmarsh (June 1, 1899 – January 18, 1963) was a leading British mathematician.
Education
Titchmarsh was educated at King Edward VII School (Sheffield) and Balliol College, Oxford, where he began his studies in October 1 ...
in 1926.
Titchmarsh convolution theorem
If
and
are integrable functions, such that
:
almost everywhere
In measure theory (a branch of mathematical analysis), a property holds almost everywhere if, in a technical sense, the set for which the property holds takes up nearly all possibilities. The notion of "almost everywhere" is a companion notion to ...
in the interval