Abstract
It is proved that a nonzero function is not in L p(R n) with p \le 2n/d if its Fourier transform is supported by a d-dimensional submanifold. It is shown that the assertion fails for p > 2n/d and d \ge n/2. The result is applied for obtaining uniqueness theorems for convolution equations in L p-spaces.
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Communicated by Carlos Berenstein.
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Agranovsky, M., Narayanan, E. L p-Integrability, Supports of Fourier Transforms and Uniqueness for Convolution Equations. J. Fourier Anal. Appl. 10, 315–324 (2004). https://doi.org/10.1007/s00041-004-0986-4
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DOI: https://doi.org/10.1007/s00041-004-0986-4