Properties of the Fourier transform in white noise analysis (Q2782773)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Properties of the Fourier transform in white noise analysis |
scientific article; zbMATH DE number 1725453
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Properties of the Fourier transform in white noise analysis |
scientific article; zbMATH DE number 1725453 |
Statements
8 April 2002
0 references
S-transform
0 references
T-transform
0 references
Hida distribution
0 references
0.91966397
0 references
0.8799838
0 references
0.86938584
0 references
0.8495409
0 references
0 references
Properties of the Fourier transform in white noise analysis (English)
0 references
The author considers the Fourier transform on the space \(S'\) of Hida distributions in the white noise theory. In analogy to classical analysis, the Fourier transform operator \(F\) is identified as the adjoint of an operator \(G\) on test functions. Here, however, the operator \(G\) does not operate like the Fourier transform. An explicit description of \(G\) is obtained and applied to prove some formulae involving the Gateaux derivative of functionals on \(S'\).
0 references
