Uniqueness of the fourier transform on the euclidean spaces and certain locally compact lie groups

Abstract

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