The Logvinenko-Sereda Theorem for the Fourier-Bessel transform
نویسندگان
چکیده
Abstract. The aim of this paper is to establish an analogue of Logvinenko-Sereda’s theorem for the Fourier-Bessel transform (or Hankel transform) Fα of order α > −1/2. Roughly speaking, if we denote by PWα(b) the Paley-Wiener space of L -functions with FourierBessel transform supported in [0, b], then we show that the restriction map f → f |Ω is essentially invertible on PWα(b) if and only if Ω is sufficiently dense. Moreover, we give an estimate of the norm of the inverse map. As a side result we prove a Bernstein type inequality for the Fourier-Bessel transform.
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