We characterize orthonormal bases, Riesz bases and frames which arise from the action of
a countable discrete group Γ on a single element ψ of a given Hilbert space H. As Γ might …

Studies of various reproducing function systems emphasized the role of translations and the
Fourier periodization function. These influenced the development of the concept of dual …

For a second countable locally compact group G and a closed abelian subgroup H, we give
a range function classification of closed subspaces in L 2 (G) invariant under left translation …

Let $ K $ be a compact group, and let $\rho $ be a representation of $ K $ on a Hilbert space
$\mathcal {H} _\rho $. We classify invariant subspaces of $\mathcal {H} _\rho $ in terms of …

Given a simply connected nilpotent Lie group having unitary irreducible representations that
are square-integrable modulo the center, we use operator-valued periodization to give a …

We present a survey of research on orbits of unitary representations developed under the
guidance and leadership of Guido Weiss in the last 20 years. This line of research started …

Let $ E (\mathscr {A}) $ denote the shift-invariant space associated with a countable family
$\mathscr {A} $ of functions in $ L^{2}(\mathbb {H}^{n}) $ with mutually orthogonal …

In this paper, twisted shift-invariant spaces in L 2 (R 2 n) are introduced. Characterizations of
orthonormal system and Bessel sequence of twisted translates in L 2 (R 2 n) are obtained in …

Frames and Riesz bases for shift invariant spaces on the abstract Heisenberg group -
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Consider a unitary dual integrable representation Π of an LCA group G on a separable
Hilbert space H. In this paper, we provide answers to several questions, centered around the …