Geodesic
The Fourier transformation of functions defined on a~Hilbert space
Matematičeskie zametki, Tome 14 (1973) no. 4, pp. 465-468.

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It is shown that one cannot define a transformation analogous to the Fourier transformation, carrying a function into a function, for functions defined on a Hilbert space. 
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     author = {V. Yu. Bentkus},
     title = {The {Fourier} transformation of functions defined on {a~Hilbert} space},
     journal = {Matemati\v{c}eskie zametki},
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     year = {1973},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_4_a0/}
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V. Yu. Bentkus. The Fourier transformation of functions defined on a~Hilbert space. Matematičeskie zametki, Tome 14 (1973) no. 4, pp. 465-468. http://geodesic.mathdoc.fr/item/MZM_1973_14_4_a0/