We study closed subspaces of L 2 (X), where (X, μ) is a σ-finite measure space, that are
invariant under the unitary representation associated to a measurable action of a discrete …

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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 …

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 …

In this work we extend classical structure and duality results in Gabor analysis on the
euclidean space to the setting of second countable locally compact abelian (LCA) groups …

In this paper we study the properties of multiplication invariant (MI) operators acting on
subspaces of the vector-valued space L 2 (X; H). We characterize such operators in terms of …

In this paper, we introduce and study the operator-valued Gabor frames on locally compact
abelian groups. We first prove a density theorem which says that for an operator-valued …

Due to the redundancy property of frames, the stable decomposition of a vector in the
separable Hilbert space H allows the flexibility of choosing different types of duals for a …

We investigate the structure of subspaces of a Hilbert space that are invariant under unitary
representations of a discrete group. We work with square integrable representations, and we …

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 …