Abstract We consider Gabor frames generated by a general lattice and window function that belongs to one of the following spaces: Sobolev space $$V_1 = H^1(\mathbb {R}^d)$$ V 1 = H ( R</mml...

Analysis `1-recovery refers to a technique of recovering a signal that is sparse in some transform domain from incomplete corrupted measurements. This includes total variation minimization as an important special case when the transform domain is generated by a difference operator. In the present paper we provide a bound on the number of Gaussian measurements required for successful recovery fo...

The notion of monotonic independence, introduced by N. Muraki, is considered in a more general frame, similar to the construction of operatorvalued free probability. The paper presents constructions for maps with similar properties to the H and K transforms from the literature, semi inner-product bimodule analogues for the monotone and weakly monotone product of Hilbert spaces, an ad-hoc versio...

Informationally complete measurements on a quantum system allow to estimate the expectation value of any arbitrary operator by just averaging functions of the experimental outcomes. We show that such kind of measurements can be achieved through positive-operator valued measures (POVM’s) related to unitary irreducible representations of a group on the Hilbert space of the system. With the help o...

The aim of this paper is to study Sobolev-type embeddings and their optimality. We work in the frame of rearrangement-invariant norms and unbounded domains. We establish the equivalence of a Sobolev embedding to the boundedness of a certain Hardy operator on some cone of positive functions. This Hardy operator is then used to provide optimal domain and range rearrangement-invariant norm in the ...

Frames which are tight might be considered optimally conditioned in the sense of their numerical stability. This leads to the question of perfect preconditioning of frames, i.e., modification of a given frame to generate a tight frame. In this paper, we analyze prefect preconditioning of frames by a diagonal operator. We derive various characterizations of functional analytic and geometric type...