Local uncertainty inequalities for locally compact groups

Price, John F. ; Sitaram, Alladi (1988) Local uncertainty inequalities for locally compact groups Transactions of the American Mathematical Society, 308 (1). pp. 105-114. ISSN 0002-9947

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Official URL: http://www.ams.org/journals/tran/1988-308-01/S0002...

Related URL: http://dx.doi.org/10.1090/S0002-9947-1988-0946433-5


Let G be a locally compact unimodular group equipped with Haar measure m, G^ its unitary dual and μ the Plancherel measure (or something closely akin to it) on G^. When G is a euclidean motion group, a noncompact semisimple Lie group or one of the Heisenberg groups we prove local uncertainty inequalities of the following type: given θ∈[O,½) there exists a constant Kθ such that for all ƒ in a certain class of functions on G and all measurable E ⊆ G^, (∫ETr(π(ƒ)π(ƒ))dμ(π)½ ≤ Kθμ(E)θ||Φθƒ||2 where Φθ is a certain weight function on G (for which an explicit formula is given). When G=Rk the inequality has been established with Φθ(x)=|x|.

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