A Beurling Theorem for Exponential Solvable Lie Groups
Copyright policy )A Beurling Theorem for Exponential Solvable Lie Groups
For an exponential solvable Lie group \(G\) with non-trivial center, the authors show that a measurable function \(f\) on \(G\) satisfying \[ \int_G\int_{\mathcal W}|f(g)|^2\|K_\xi^{1/2}\pi_\xi(f)\|^2_{HS} e^{2\|g\|\|\xi\|}\,dg\,d\xi<\infty \] is 0 a.e. Here the integral over the cross section \(\mathcal W\) of coadjoint orbits is as in the Plancherel formula for exponential Lie groups. This result extends a theorem of Beurling [\textit{L. Hörmander}, Ark. Mat. 29, No. 2, 237--240 (1991; Zbl 0755.42009)] to this class of Lie groups.
uncertainty principle, Plancherel formula, solvable exponential Lie groups, Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.), Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
uncertainty principle, Plancherel formula, solvable exponential Lie groups, Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.), Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
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