The problem of exact null-controllability is considered for a wide class of linear neutral-type systems with distributed delay. The main tool of the analysis is the application of the moment problem approach and the theory of the basis property of exponential families. A complete characterization of this problem is given. The minimal time of controllability is specified. The results are based o...

We show how it is possible to diagonalize a certain class of homogeneous linear operators in a biorthogonal wavelet basis. Given a linear operator and a biorthogonal wavelet basis we construct a new biorthog-onal wavelet basis such that by analyzing a function in the new basis and multiplying the wavelet coeecients by a scale dependent factor we get the wavelet coeecients of the transformed fun...

Let H be a (separable) Hilbert space and {ek}k≥1 a fixed orthonormal basis of H. Motivated by many papers on scaled projections, angles of subspaces and oblique projections, we define and study the notion of compatibility between a subspace and the abelian algebra of diagonal operators in the given basis. This is used to refine previous work on scaled projections, and to obtain a new characteri...

Let B be a unital commutative semi-simple Banach algebra. We study endomorphisms of B which are simultaneously Riesz operators. Clearly compact and power compact endomorphisms are Riesz. Several general theorems about Riesz endomorphisms are proved, and these results are then applied to the question of when Riesz endomorphisms of certain algebras are necessarily power compact.

We construct bivariate local trigonometric bases on a \two-overlapping" triangular grid. A main result is the description of various trigonometric bases on triangles, satisfying parity conditions at the edges. Moreover, we introduce folding operators for the triangular grid. From these results we derive assertions on Riesz stability and the bi-orthogonal basis.

The closed-loop form of a second-order hyperbolic system with scalar collocated sensor/actuator is considered. The Riesz basis property of the system is verified for diagonal semigroups based on an abstract result of one rank perturbation of discrete-type operators in Hilbert spaces. A simplified proof for the abstract result is presented.