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Cyclic subspaces for unitary representations of LCA groups; generalized Zak transform

Eugenio Hernández;  Hrvoje Šikić;  Guido Weiss;  Edward Wilson — 2010

Colloquium Mathematicae

We just published a paper showing that the properties of the shift invariant spaces, ⟨f⟩, generated by the translates by ℤⁿ of an f in L²(ℝⁿ) correspond to the properties of the spaces L²(𝕋ⁿ,p), where the weight p equals [f̂,f̂]. This correspondence helps us produce many new properties of the spaces ⟨f⟩. In this paper we extend this method to the case where the role of ℤⁿ is taken over by locally compact abelian groups G, L²(ℝⁿ) is replaced by a separable Hilbert space on which a unitary representation...

Isospectral deformations of closed riemannian manifolds with different scalar curvature

Carolyn S. Gordon;  Ruth Gornet;  Dorothee Schueth;  David L. Webb;  Edward N. Wilson — 1998

Annales de l'institut Fourier

We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds , more precisely, on S n × T m , where T m is a torus of dimension m ≥ 2 and S n is a sphere of dimension n ≥ 4 . These metrics are not locally homogeneous; in particular, the scalar curvature of each metric is nonconstant. For some of the deformations, the maximum scalar curvature changes during the deformation.

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