Explicit cross-sections of singly generated group actions

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dc.creatorLarson, David
dc.creatorSchulz, Eckart
dc.creatorSpeegle, Darrin
dc.creatorTaylor, Keith
dc.date2006-04-28
dc.date.accessioned2026-07-07T07:11:23Z
dc.date.available2026-07-07T07:11:23Z
dc.descriptionWe consider two classes of actions on $\mathbb{R}^n$ - one continuous and one discrete. For matrices of the form $A = e^B$ with $B \in M_n(\R)$, we consider the action given by $γ\to γA^t$. We characterize the matrices $A$ for which there is a cross-section for this action. The discrete action we consider is given by $γ\to γA^k$, where $A\in GL_n(\R)$. We characterize the matrices $A$ for which there exists a cross-section for this action as well. We also characterize those $A$ for which there exist special types of cross-sections; namely, bounded cross-sections and finite measure cross-sections. Explicit examples of cross-sections are provided for each of the cases in which cross-sections exist. Finally, these explicit cross-sections are used to characterize those matrices for which there exist MSF wavelets with infinitely many wavelet functions. Along the way, we generalize a well-known aspect of the theory of shift-invariant spaces to shift-invariant spaces with infinitely many generators.
dc.identifierhttps://arxiv.org/abs/math/0604638
dc.identifierhttp://arxiv.org/abs/math/0604638
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111734
dc.subjectFunctional Analysis
dc.subject42C40
dc.titleExplicit cross-sections of singly generated group actions
dc.typetext

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