Uniqueness of the Fourier transform on the Euclidean spaces and certain locally compact Lie groups
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We explored the Heisenberg uniqueness pairs corresponding to the spiral, hyperbola, circle, cross, exponential curves, and surfaces. Then, we prove a characterization of the Heisenberg uniqueness pairs corresponding to four parallel lines. We observe that the size of the determining sets for X depends on the number of lines and their irregular distribution that further relates to a phenomenon of interlacing of the zero sets of certain trigonometric polynomials.
Supervisor: Rajesh K. Srivastava