"Maximal cyclic subspaces for dual integrable representations"Slamic, IvanaIn the theory of wavelets, maximal principal shift-invariant spaces play an important role. Maximality is characterized by the strict positivity of the periodization function, the property which also appears in the characterization of several independence and basis related properties for the system of integer translates. We consider the concept in a more general setting of LCA groups and unitary dual integrable representations. We describe the dual integrable triples which allow a decomposition of the Hilbert space into an orthogonal sum of n maximal cyclic subspaces and analyze how the questions concerned with maximality are reflected in redundancy and basis related properties of the generating orbit. Of particular interest is the case when n=1, i.e., when the generating orbit is complete in the whole space. This is joint work with Hrvoje Sikic. |
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