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A Plancherel-type theorem for Boehmians. (English) Zbl 1208.46041

The advent of Boehmians extended the classical theory of the Fourier transform on function spaces or generalized function spaces (distributions) in the context of Boehmian spaces. The authors construct a Boehmian space which contains Fourier transforms of elements of certain classical Sobolev spaces and define their Fourier-Plancherel transform. The image is also characterized as certain \(H^s\) distributions, which (in particular) characterizes Fourier-Plancherel transforms of the same local distributions as convolution quotients of certain specific functions.

MSC:

46F12 Integral transforms in distribution spaces
46F10 Operations with distributions and generalized functions
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