Lp-Integrability, Supports of Fourier Transforms and Uniqueness for Convolution Equations
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- Agranovsky, M. & Narayanan, E. J. Fourier Anal. Appl. (2004) 10: 315. doi:10.1007/s00041-004-0986-4
It is proved that a nonzero function is not in Lp(Rn) 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 Lp-spaces.