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In ], an '''ultradistribution''' is a ] that extends the concept of a ] by allowing ] whose ]s have ]. They form an element of the ] 𝒵′, where 𝒵 is the space of test functions whose Fourier transforms belong to 𝒟, the space of ] with compact support. In ], an '''ultradistribution''' is a ] that extends the concept of a ] by allowing ] whose ]s have ]. They form an element of the ] 𝒵′, where 𝒵 is the space of test functions whose Fourier transforms belong to 𝒟, the space of ] with compact support.


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In functional analysis, an ultradistribution 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

References

  • Hoskins, R. F.; Sousa Pinto, J. (2011). Theories of generalized functions: Distributions, ultradistributions and other generalized functions (2nd ed.). Philadelphia: Woodhead Publishing.
  • Vilela Mendes, Rui (2012). "Stochastic solutions of nonlinear PDE's and an extension of superprocesses". arXiv:1209.3263.
  • Hasumi, Morisuke (1961). "Note on the n-tempered ultra-distributions". Tohoku Mathematical Journal. 13 (1): 94–104. doi:10.2748/tmj/1178244274.
  • 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.


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