nLab ultradistribution

Ultradistribution is an element of the space $\mathcal{Z}'$ dual to the space $\mathcal{Z}$ of test functions whose Fourier transform is in the space $\mathcal{D}$ of infinitely differentiable functions of compact support.

Related $n$Lab pages include distribution

• R. F. Hoskins, J. Sousa Pinto, Theories of generalized functions: Dis- tributions, ultradistributions and other generalized functions, 2nd. edition Woodhead Publ., Philadelphia 2011.
• Rui Vilela Mendes, Stochastic solutions of nonlinear PDE’s and an extension of superprocesses, arxiv/1209.3263
• Morisuke Hasumi, Note on the $n$-tempered ultra-distributions, Tohoku Math. J. (2) 13 (1961), no. 1, 94–104 doi euclid
• J. Sousa Pinto, R. F. Hoskins, A nonstandard definition of finite order ultradistributions, Proc. Indian Acad. Sci. - Mathematical Sciences (1999) 109:4, pp 389–395 doi

category: analysis