科研之友
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摘要
Let N be a step two connected and simply connected non commutative nilpotent Lie group which is square-integrable modulo the center. Let Z be the center of N. Assume that N = P x M such that P and M are simply connected, connected abelian Lie groups, P is a maximal normal abelian subgroup of N, M acts non-trivially on P by automorphisms and dim P/Z = dim M. We study bandlimited subspaces of L-2 (N) which admit Parseval frames generated by discrete translates of a single function. We also find characteristics of bandlimited subspaces of L-2(N) which do not admit a single Parseval frame. We also provide some conditions under which continuous wavelets transforms related to the left regular representation admit discretization, by some discrete set Gamma subset of N. Finally, we show some explicit examples in the last section.
- 出版日期2014
