Shift-invariant spaces form a fundamental class of function spaces where elements can be represented as linear combinations of translates of one or more generating functions. This concept is pivotal ...

The study of shift-invariant systems and abelian groups underpins several modern advances in harmonic analysis, signal processing and pure mathematics. At its core, this area explores how translation ...

In this note, we observe that the dimension function associated with a wavelet system is the trace of the Gramian fibers of the shift-invariant system generated by the negative dilations of the mother ...

This is a preview. Log in through your library . Abstract If b ∈ B(H∞), the unit ball of H∞, then the de Branges-Rovnyak space ℋ(b) is a Hilbert space contained contractively in H2 that is invariant ...