Vignon Oussa

Bandlimited Spaces on Some 2-step Nilpotent Lie Groups With One Parseval Frame Generator

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 ⋊M such that P, and M are simply connected, connected abelian Lie groups, M acts non-trivially on P by automorphisms and dimP/Z = dimM. We study band-limited subspaces of L 2 (N) which admit Parseval frames generated by discrete translates of a single function. We also find characteristics of band-limited 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 ⊂ N. Finally, we show some explicit examples in the last section.

Sinc-type Functions on a Class of Nilpotent Lie Groups

Abstract. Let N be a simply connected, connected nilpotent Lie group with the following assumptions. Its Lie algebra 𝔫

Computing Vergne polarizing subalgebras

{\mathfrak {n}}

Regular Sampling on Metabelian Nilpotent Lie Groups: The Multiplicity-Free Case

is an n-dimensional vector space over the reals. Moreover, 𝔫=𝔷⊕𝔟⊕𝔞

Dihedral Group Frames which are Maximally Robust to Erasures

{\mathfrak {n=z}\oplus \mathfrak {b}\oplus \mathfrak {a}}

Dihedral Group Frames with the Haar Property

, 𝔷

Gabor orthonormal bases generated by indicator functions of parallelepiped-shaped sets

{\mathfrak {z}}

Sampling and interpolation on certain nilpotent lie groups

is the center of 𝔫

Characterization of Shift-Invariant Spaces on a Class of Nilpotent Lie Groups with Applications

{\mathfrak {n}}

Sampling and Interpolation on Some Nilpotent Lie Groups

, 𝔷=ℝZ n-2d ⊕ℝZ n-2d-1 ⊕⋯⊕ℝZ 1