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Geller, Daryl

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

J. Funct. Anal. 36, 205-254 (1980).
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Cited in 5 Reviews
Cited in 40 Documents

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

Keywords:

Heisenberg group; Schwartz space; Fourier transform; group contraction; division problem for convolution; Hardy space
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\textit{D. Geller}, J. Funct. Anal. 36, 205--254 (1980; Zbl 0433.43008)
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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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.