It is proved that a nonzero function is not in Lp(Rn) with p ≤ 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 ≥ n/2. The result is applied for obtaining uniqueness theorems for convolution equations in Lp-spaces.
- Convolution equations
- Evolution equations
- Supports of fourier transforms