In functional analysis, an ultradistribution (also called an ultra-distribution[1]) is a generalized function that extends the concept of a distributions by allowing test functions whose Fourier transforms have compact support.
[2] They form an element of the dual space 𝒵′, where 𝒵 is the space of test functions whose Fourier transforms belong to 𝒟, the space of infinitely differentiable functions with compact support.
[3]
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