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Abstract It was one of great successes of Kirillov's orbit method to see that the unitary dual of an exponential Lie group is in bijective correspondence with the orbit space associated with the linear dual of the Lie algebra of the group in question. To show that this correspondence is an...
Abstract This is essentially a survey on tube domains over irreducible symmetric cones or their bounded realizations. It includes the fact that in rank 2 these inequalities have now been proved for the whole range of possible exponents p , due to recent work of Bourgain and Demeter. We also...
Abstract So far, the uncertainty principles for solvable non-exponential Lie groups have been treated only in few cases. The first author and Kaniuth produced an analogue of Hardy's theorem for a diamond Lie group, which is a semi-direct product of ℝ d with the Heisenberg group ℍ 2 d + 1...
Abstract We prove various versions of uncertainty principles for a certain Fourier transform ℱ A . Here, A is a Chébli function (that is, a Sturm–Liouville function with additional hypotheses). We mainly establish an analogue of Beurling's theorem, and its relatives such as theorems of...
Abstract We consider a random matrix X uniformly distributed on an orbit for the action of the orthogonal group on the space of real symmetric matrices or of the unitary group on the space of Hermitian matrices. The problem is to evaluate the distribution of the eigenvalues of a compression of X...
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