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Characterization of Fourier transform of $H$-valued functions on the real line

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A characterization is obtained for the Fourier transform of functions belonging to ℒ2(ℝ,H), where H denotes a Hilbert C∗-module. But in the case of functions belonging to L1(ℝ,H) a similar… Click to show full abstract

A characterization is obtained for the Fourier transform of functions belonging to ℒ2(ℝ,H), where H denotes a Hilbert C∗-module. But in the case of functions belonging to L1(ℝ,H) a similar result is proved when H is a separable Hilbert space.

Keywords: characterization; valued functions; transform valued; fourier transform; functions real; characterization fourier

Journal Title: Rocky Mountain Journal of Mathematics
Year Published: 2021

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