A note on the convolution theorem for the Fourier transform

作者:Kahane Charles S*
来源:Czechoslovak Mathematical Journal, 2011, 61(1): 199-207.
DOI:10.1007/s10587-011-0006-1

摘要

In this paper we characterize those bounded linear transformations Tf carrying L (1)(a"e(1)) into the space of bounded continuous functions on a"e(1), for which the convolution identity T(f * g) = Tf center dot Tg holds. It is shown that such a transformation is just the Fourier transform combined with an appropriate change of variable.

  • 出版日期2011-3

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