That is to say that " ? " is an identity element for the convolution on tempered distributions, and in fact the space of compactly supported distributions under convolution is an associative algebra with identity the delta function.
32.
The Gaussian cylinder set measure on " H " gives a cylinder set measure on the space of tempered distributions, which extends to a measure on the space of tempered distributions, " S " & prime;.
33.
The Gaussian cylinder set measure on " H " gives a cylinder set measure on the space of tempered distributions, which extends to a measure on the space of tempered distributions, " S " & prime;.
34.
More generally, every continuous translation invariant continuous linear operator on " L " " p " for 1 d " " p " < " is the convolution with a tempered distribution whose Fourier transform is bounded.
35.
Use of the space of smooth, rapidly ( faster than any polynomial increases ) decreasing test functions ( these functions are called Schwartz functions ) gives instead the tempered distributions, which are important because they have a well-defined distributional Fourier transform.
36.
In mathematics, a "'Dirac comb "'( also known as an "'impulse train "'and "'sampling function "'in electrical engineering ) is a tempered distribution constructed from Dirac delta functions
37.
As a matter of fact the FT is a bijection of a very large functional domain into itself; this is the space of all tempered distributions ( in this big pot you may find functions but also measures, distributional derivatives of measures, etc ).
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