Ultradistribution

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Wikipedia

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 𝒡′, where 𝒡 is the space of test functions whose Fourier transforms belong to π’Ÿ, the space of infinitely differentiable functions with compact support.[3]

See also

References

  1. ↑ Hasumi, Morisuke (1961). "Note on the n-tempered ultra-distributions". Tohoku Mathematical Journal. 13 (1): 94–104. doi:10.2748/tmj/1178244274 (inactive 1 July 2025).{{cite journal}}: CS1 maint: DOI inactive as of July 2025 (link)
  2. ↑ Hoskins, R. F.; Sousa Pinto, J. (2011). Theories of generalized functions: Distributions, ultradistributions and other generalized functions (2nd ed.). Philadelphia: Woodhead Publishing.
  3. ↑ Sousa Pinto, J.; Hoskins, R. F. (1999). "A nonstandard definition of finite order ultradistributions". Proceedings of the Indian Academy of Sciences – Mathematical Sciences. 109 (4): 389–395. doi:10.1007/BF02837074.

Further reading

  • Vilela Mendes, Rui (2012). "Stochastic solutions of nonlinear PDE's and an extension of superprocesses". arXiv:1209.3263 [math-ph].