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Fourier analysis on the Heisenberg group. I. Schwartz space. (English) Zbl 0433.43008

MSC:
 43A80 Analysis on other specific Lie groups 22E30 Analysis on real and complex Lie groups 43A17 Analysis on ordered groups, $$H^p$$-theory 43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups 46E10 Topological linear spaces of continuous, differentiable or analytic functions
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References:
 [1] Bargmann, V, On a Hilbert space of analytic functions and an associated integral transform, Comm. pure appl. math., 14, 187-214, (1961) · Zbl 0107.09102 [2] Fefferman, C; Stein, E.M, Hp spaces of several variables, Acta math., 129, 137-193, (1972) · Zbl 0257.46078 [3] Folland, G.B; Stein, E.M, Estimates for the $$\̄$$t6_{b} complex and analysis on the Heisenberg group, Comm. pure appl. math., 27, 429-522, (1974) · Zbl 0293.35012 [4] Geller, D, Fourier analysis on the Heisenberg group, (), 1328-1331 · Zbl 0351.43012 [5] Geller, D, Some results in Hp theory for the Heisenberg group, Duke math. J., (1980), in press [6] {\scD. Geller}, Local solvability and homogeneous distributions on the Heisenberg group, Comm. in PDE, to appear. · Zbl 0488.22020 [7] Greiner, P.C; Kohn, J.J; Stein, E.M, Necessary and sufficient conditions for solvability of the lewy equation, (), 3287-3289 · Zbl 0308.35017 [8] Inonu, E; Wigner, E.P, On the contraction of groups and their representations, (), 510-524 · Zbl 0050.02601 [9] Lewy, H, An example of a smooth linear partial differential equation without solution, Ann. of math., 66, 155-158, (1957) · Zbl 0078.08104 [10] Reed, M; Simon, B, () [11] {\scC. Rockland}, Hypoellipticity on the Heisenberg group—representation-theoretic criteria. · Zbl 0326.22007
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