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 ...

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 ...

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 ...

In this short note, we prove that a bi-invariant Riemannian metric on Sp(n) is uniquely determined by the spectrum of its Laplace–Beltrami operator within the class of left-invariant metrics on Sp(n). In other words, on ...

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 ...

In this article we study the structure of Γ-invariant spaces of L2(S). Here S is a second countable LCA group. The invariance is with respect to the action of Γ, a non commutative group in the form of a semidirect product ...

An emergent trend in quantum computation is the topological quantum computation (TQC). Briefly, TQC results from the application of quantum computation with the aim to solve the problems of quantum topology such as topological ...