This article generalizes recent results in the extra invariance for shift-invariant spaces to the context of LCA groups. Let G be a locally compact abelian (LCA) group and K a closed subgroup of G. A closed subspace of ...

In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed ...

Let H be Hilbert space and (Ω, m) a σ-finite measure space. Multiplicatively invariant(MI) spaces are closed subspaces of L2(Ω, H) that are invariant under point-wise multiplication byfunctions from a fixed subset of L∞(Ω). ...

A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper ...

Given an arbitrary finite set of data F = {f1, ..., fm} ⊂ L2(Rd) we prove the existence and show how to construct a “small shift invariant space” that is “closest” to the data F over certain class of closed subspaces of ...

A (K,Λ) shift-modulation invariant space is a subspace of L2(G) that is invariant under translations along elements in K and modulations by elements in Λ. Here G is a locally compact abelian group, and K and Λ are closed ...

A finitely generated shift invariant space V is a closed subspace of L2(Rd) that can be generated by the integer translates of a finite number of functions. A set of frame generators for V is a set of functions whose integer ...

Given discrete groups Γ ⊂ Δ we characterize (Γ , σ) -invariant spaces that are also invariant under Δ. This will be done in terms of subspaces that we define using an appropriate Zak transform and a particular partition ...

© 2021, The Hebrew University of Jerusalem.It is well known that the space of invariant probability measures for transitive sub-shifts of finite type is a Poulsen simplex. In this article we prove that in the non-compact ...

In this note we study the structure of shift-preserving operators acting on a finitely generated shift-invariant space. We define a new notion of diagonalization for these operators, which we call s-diagonalization. We ...