In a first part, we are concerned with the relationships between polynomials in the two generators of the algebra of Heisenberg–Weyl, its Bargmann–Fock representation with differential operators and the associated one-parameter group. Upon this basis, the paper is then devoted to the groups of Riordan matrices associated to the related transformations of matrices (i.e., substitutions with prefu...

We give a formula for the one-parameter strongly continuous semigroup e−tL, t > 0, generated by the Hermite operator L on the Heisenberg group H1 in terms of Weyl transforms, and use it to obtain an L2 estimate for the solution of the initial value problem for the heat equation governed by L in terms of the Lp norm of the initial data for 1 ≤ p ≤ ∞. This research has been partially supported by...

We consider parameter-elliptic boundary value problems and uniform a priori estimates in Lp-Sobolev spaces of Bessel potential and Besov type. The problems considered are systems of uniform order and mixed-order systems (Douglis-Nirenberg systems). It is shown that compatibility conditions on the data are necessary for such estimates to hold. In particular, we consider the realization of the bo...

The main purpose of the present note is to show (Theorem 2) that any regular ©-class of any semigroup is a partial homomorphic image of a Brandt groupoid. It follows from this that a semigroup with zero is a partial homomorphic image of a Brandt semigroup if and only if it is regular and O-bisimple. In the first section, an alternative formulation is given of the determination by H.-J. Hoehnke ...

This paper addresses the boundary control for flutter suppression of a flexible wing, both in bending and twisting displacements, under unsteady aerodynamic loads. The wing is modeled by a distributed parameter system described as two coupled partial differential equations. The problem is tackled in the framework of semigroup theory, and a Lyapunov-based stability analysis is carried out to ass...

One of our main results is the following convergence theorem for one-parameter nonexpansive semigroups: let C be a bounded closed convex subset of a Hilbert space E, and let {T(t) : t ∈ R+} be a strongly continuous semigroup of nonexpansive mappings on C. Fix u ∈ C and t1, t2 ∈ R+ with t1 < t2. Define a sequence {xn} in C by xn = (1− αn)/ (t2 − t1) ∫ t2 t1 T(s)xnds+ αnu for n ∈N, where {αn} is ...

Abstract. The aim of this paper is to give an existence theorem for a semilinear equation of evolution in the case when the generator of semigroup of operators depends on time parameter. The paper is a generalization of [2]. Basing on the notion of a measure of noncompactness in Banach space, we prove the existence of mild solutions of the equation considered. Additionally, the applicability of...

The viscous quantum hydrodynamic model derived for semiconductor simulation is studied in this paper. The principal part of the vQHD system constitutes a parameter–elliptic operator provided that boundary conditions satisfying the Shapiro–Lopatinskii criterion are specified. We classify admissible boundary conditions and show that this principal part generates an analytic semigroup, from which ...

Throughout this paper we denoted by and the set of all positive integers and all positive real numbers, respectively. Let X be a real Banach space, and let C be a nonempty closed convex subset ofX. Amapping T ofC into itself is said to be nonexpansive if ‖Tx−Ty‖ ≤ ‖x−y‖ for each x, y ∈ C. We denote by F T the set of fixed points of T . We know that F T is nonempty ifC is bounded; for more detai...

In a first part, we are concerned with the relationships between polynomials in the two generators of the algebra of Heisenberg–Weyl, its Bargmann–Fock representation with differential operators and the associated one-parameter group. Upon this basis, the paper is then devoted to the groups of Riordan matrices associated to the related transformations of matrices (i.e. substitutions with prefun...