A generalization of the Paley–Wiener theorem for Mellin transforms and metric characterization of function spaces
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AbstractWe characterize the function space whose elements have a Mellin transform with exponential decay at infinity. This result can be seen as a generalization of the Paley–Wiener theorem for Mellin transforms. As a byproduct in a similar spirit, we also characterize spaces of functions whose distances from Mellin–Paley–Wiener spaces have a prescribed asymptotic behavior. This leads to Mellin–Sobolev type spaces of fractional order.
2019 ◽
Vol 276
(2)
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pp. 636-657
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1999 ◽
pp. 183-191
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