Bandlimited spaces on some 2-step nilpotent Lie groups with one Parseval frame generator (Q470410)

The author studies the bandlimited subspaces of \(L^2(N)\) which admit Parseval frames generated by discrete translates of a single function where \(N\) is a step two connected and simply connected non-commutative nilpotent Lie group which is square-integrable modulo the center. The following assumptions are made.NEWLINENEWLINE(i) The center is denoted by \(Z\).NEWLINENEWLINE(ii) \(N=P\times M\) such that \(P\) and \(M\) are simply connected, connected abelian Lie groups.NEWLINENEWLINE (iii) \(P\) is a maximal normal abelian subgroup of \(N\).NEWLINENEWLINE (iv) \(M\) acts non-trivially on \(P\) by automorphisms.NEWLINENEWLINE (v) dim\(P/Z=\) dim M.NEWLINENEWLINEThe author also finds characteristics of bandlimited subspaces of \(L^2(N)\) which do not admit a single Parseval frame. Examples are provided.