The concept of linear Schrödinger representation of the real Heisenberg nilpotent group and its various realizations is used to link the theory of radar ambiguity functions with nilpotent harmonic analysis. This group-representation theoretic approach allows us to analyze the radar ambiguity functions simultaneously in time and frequency. Moreover, it allows us to determine the group of all transformations that leave the radar ambiguity surfaces invariant and to specify all admissible envelope functions that belong to radar signals of the same finite energy. In particular, an investigation of the radial, i.e., S0(2, R )-invariant radar ambiguity surfaces, gives rise to an identity for Laguerre-Weber functions of different orders, which implies on its part an identity for holomorphic theta series.
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Walter Schempp (1984) studied this question.