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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Radar ambiguity functions, the Heisenberg group, and holomorphic theta series
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by Walter Schempp PDF
Proc. Amer. Math. Soc. 92 (1984), 103-110 Request permission

Abstract:

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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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 92 (1984), 103-110
  • MSC: Primary 22E25; Secondary 22E30, 33A75, 43A80, 60G35, 81D05, 94A12
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0749901-6
  • MathSciNet review: 749901