for all f ∈ H. In general Banach spaces one cannot use just the equivalence of norms similar to (1.1). The above construction breaks down because, in this case, the analysis operator ends up being bounded below and not necessarily left invertible. As a result a “frame decomposition” remains possible but “frame reconstruction” no longer makes sense. In case of localizaed frames, however, this ob...

Within front-form dynamics and in the Breit frame where initial and final three-momenta of the system are directed along the z axis, Poincaré covariance constrains the current operator only through kinematical rotations around the z axis. Therefore, in this frame the current can be taken in the one-body form. Applications to deep inelastic structure functions in an exactly solvable model and to...

This paper extends the e cient factorization of the Gabor frame operator developed by Strohmer in [17] to the Gabor analysis/synthesis operator. The factorization provides a fast method for computing the discrete Gabor transform (DGT) and several algorithms associated with it. The factorization algorithm should be used when the involved window and signal have the same length. An optimized imple...

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...

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...

We define an interpretation of modal languages with polyadic operators in modal languages that use monadic operators (diamonds) only. We also define a simulation operator which associates a logic Λ in the diamond language with each logic Λ in the language with polyadic modal connectives. We prove that this simulation operator transfers several useful properties of modal logics, such as finite/r...

A central problem of dynamical systems theory is to identify a reduced description of the dynamical process one can deal easier. In this paper we present a systematic method of identifying those closed sub-systems of a given discrete time dynamical system in the frame of operator theory. It is shown that this problem is closely related to finding invariant sigma algebras of the dynamics. Index ...

Abstract Phase retrieval in dynamical sampling is a novel research direction, where an unknown signal has to be recovered from the phaseless measurements with respect frame, i.e., sequence of vectors constructed by repeated action operator. The loss phase here turns well-posed into severe ill-posed inverse problem. In existing literature, involved operator usually completely known. this paper, ...

Given a discrete group and a unitary representation on a Hilbert space H, we prove that the notions of operator Bracket map and Gramian coincide on a dense set of H. As a consequence, combining this result with known frame theory, we can recover in a simple way all previous Bracket characterizations of Riesz and frame sequences generated by a single element under a unitary representation.

We prove fourteen equivalent conditions for a set of time-frequency shifts on a lattice Λ, {e2g(t − λ1) : (λ1, λ2) ∈ Λ} ⊆ L (R), to be a frame for L(R). Remarkably, several of these conditions can be formulated without an inequality. In particular, instead of checking the invertibility of the frame operator on L(R), it suffices to verify that it is one-to-one on a certain subspace of tempered d...