Radar Ambiguity Functions, the Heisenberg Group, and Holomorphic Theta Series

DOI10.2307/2045164zbMath0525.43007OpenAlexW4232210309MaRDI QIDQ3039895

Walter Johannes Schempp

Publication date: 1984

Full work available at URL: https://doi.org/10.2307/2045164

zbMATH Keywords

Schrödinger representationradar ambiguity functionsholomorphic theta seriesHeisenberg nilpotent groupLaguerre-Weber functionsSO(2,R)-invariant

Mathematics Subject Classification ID

Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) Analysis on other specific Lie groups (43A80)

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Quantum theta functions and Gabor frames for modulation spaces ⋮ A decomposition theorem for singular control systems on Lie groups. ⋮ Bounded \(K\)-spherical functions on Heisenberg groups ⋮ Continuity properties of the Gabor frame operator ⋮ Quantum holography and neurocomputer architectures ⋮ Neurocomputer architectures ⋮ Spaces of type \(W\), growth of Hermite coefficients, Wigner distribution, and Bargmann transform ⋮ Classical and quantum Heisenberg groups, their representations and applications ⋮ Analytic representations with theta functions for systems on ℤ(d) and on 𝕊 ⋮ Local Uncertainty Inequalities for Locally Compact Groups ⋮ Image analysis by wavelet-type transforms: Group theoretic approach

Cites Work

• Attenuation factors and nilpotent harmonic analysis
• Quantum mechanics and partial differential equations
• Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
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