The generalized translation invariant (GTI) systems unify the discrete frame theory of
generalized shift-invariant systems with its continuous version, such as wavelets, shearlets …

We introduce a family of quasi-Banach spaces—which we call wave packet smoothness
spaces—that includes those function spaces which can be characterised by the sparsity of …

Due to their adaptive nature, empirical wavelets had several successes in many fields from
engineering, science, medical signal/image processing. Recently, a general theoretical …

We consider the question whether, given a countable family of lattices (Γ j) j∈ J in a locally
compact abelian group G, there exist functions (gj) j∈ J such that the resulting generalized …

The wave packet systems are generated by the combined action of translation, dilation and
modulation on a single function while frames are basis-like systems that span a vector space …

We derive an extension of the Walnut–Daubechies criterion for the invertibility of frame
operators. The criterion concerns general reproducing systems and Besov-type spaces. As …

A method for constructing non-uniform filter banks is presented. Starting from a uniform
system of translates, generated by a prototype filter, a non-uniform covering of the frequency …

This paper considers the local integrability condition for generalised translation-invariant
systems and its relation to the Calderón integrability condition, the temperateness condition …

We prove sharp upper and lower bounds for generalized Calderón's sums associated to
frames on LCA groups generated by affine actions of cocompact subgroup translations and …

A method for constructing non-uniform filter banks is presented. Starting from a uniform
system of translates, generated by a prototype filter, a non-uniform covering of the frequency …