We consider the natural generating system for a cyclic subspace of a Hilbert space generated by a dual integrable unitary representation of a countable abelian group. We prove, under mild hypothesis, that whenever the generating system is a quasi-greedy basis it must also be an unconditional Riesz basis. A number of applications to Gabor systems and to general Vilenkin systems are considered. I...

Let (A,Ao) be a topological quasi *-algebra, which means in particular that Ao is a topological *-algebra, dense in A. Let πo be a *-representation of Ao in some pre-Hilbert space D ⊂ H. Then we present several ways of extending πo, by closure, to some larger quasi *-algebra contained in A, either by Hilbert space operators, or by sesquilinear forms on D. Explicit examples are discussed, both a...

A quantum version of Bochner’s theorem characterising Fourier transforms of probability measures on locally compact Abelian groups gives a characterisation of the Fourier transforms of Wigner quasi-joint distributions of position and momentum. An analogous quantum Bochner theorem characterises quasi-joint distributions of components of spin. In both cases quantum states in which a true distribu...

We investigate int-amplified endomorphisms on normal projective surfaces. prove that the output of equivariant MMP is either a Q-abelian surface, (equivariant) quasi-étale quotient smooth Mori dream space, or cone an elliptic curve.

The paper considers the principles of parallelization at marshalling yards and determines their importance. There are presented methods for direct decompositions torsion-free Abelian groups finite rank. applied concepts “conditionally linear graphs” depicting railway trains characteristics, including “quasi-length”, which characterizes length corresponding “quasi-graph”. has been formalized a g...

It is well known that every normed (even quasibarrelled) space a Mackey space. However, in the more general realm of locally quasi-convex abelian groups an analogous result does not hold. We give first examples spaces which are groups.