Abstract
The classical Paley-Wiener theorem for functions in L 2dx relates the growth of the Fourier transform over the complex plane to the support of the function. In this work we obtain Paley-Wiener type theorems where the Fourier transform is replaced by transforms associated with self-adjoint operators on L 2dμ , with simple spectrum, where dμ is a Lebesgue-Stieltjes measure. This is achieved via the use of support preserving transmutations.
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Communicated by Paul L. Butzer
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Boumenir, A., Nashed, M.Z. Paley-Wiener type theorems by transmutations. The Journal of Fourier Analysis and Applications 7, 395–417 (2001). https://doi.org/10.1007/BF02514504
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DOI: https://doi.org/10.1007/BF02514504