In functional analysis, an ultradistribution (also called an ultra-distribution) is a generalized function that extends the concept of a distributions by allowing test functions whose Fourier transforms have compact support. 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.
See also Distribution (mathematics) Generalized function
References
Further reading Vilela Mendes, Rui (2012). "Stochastic solutions of nonlinear PDE's and an extension of superprocesses". arXiv:1209.3263 [math-ph].