Ultradistribution
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 đ”âČ, where đ” is the space of test functions whose Fourier transforms belong to đ, the space of infinitely differentiable functions with compact support.[3]
See also
[edit]References
[edit]- â Hasumi, Morisuke (1961). "Note on the n-tempered ultra-distributions". Tohoku Mathematical Journal. 13 (1): 94â104. doi:10.2748/tmj/1178244274 (inactive 1 July 2025).
{{cite journal}}: CS1 maint: DOI inactive as of July 2025 (link) - â Hoskins, R. F.; Sousa Pinto, J. (2011). Theories of generalized functions: Distributions, ultradistributions and other generalized functions (2nd ed.). Philadelphia: Woodhead Publishing.
- â Sousa Pinto, J.; Hoskins, R. F. (1999). "A nonstandard definition of finite order ultradistributions". Proceedings of the Indian Academy of Sciences â Mathematical Sciences. 109 (4): 389â395. doi:10.1007/BF02837074.
Further reading
[edit]- Vilela Mendes, Rui (2012). "Stochastic solutions of nonlinear PDE's and an extension of superprocesses". arXiv:1209.3263 [math-ph].
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