Let A and M be closed linear operators defined on a complex Banach space X. Using operator-valued Fourier multipliers theorems, we obtain necessary and sufficient conditions to guarantee existence and uniqueness of periodic solutions to the equation d dt (Mu(t)) = Au(t) + f(t), in terms of either boundedness or R-boundedness of the modified resolvent operator determined by the equation. Our res...

A general boundedness result is given for the feedback interconnection of two nonlinear stable systems. Using the same input–output approach as in the standard small-gain theorem, the sufficient condition given here relaxes the finite-gain stability assumption and does not require a boundedness result for all possible bounded exogenous inputs. This condition has a simple graphical interpretatio...

Recently there has been a great deal of interest in studying the behaviour of rational difference equations. One of the properties which has attracted considerable attention from the experts in the research field is the boundedness character (see, e.g. [1–32] and the related references therein). This paper studies the boundedness character of positive solutions of the recursive equation yn = A+...

In this presentation the decidability issues of formalisms that allow Petri nets as tokens are studied. Especially for “elementary object-net systems” defined by Valk the decidability of the reachability and the boundedness problem is considered. It is shown that reachability becomes undecidable while boundedness remains decidable for elementary object-net systems. Furthermore it is shown that ...

In this paper, we obtain a sucient condition for boundedness of composition operators betweenweighted spaces of holomorphic functions on the upper half-plane whenever our weights are standardanalytic weights, but they don't necessarily satisfy any growth condition.

Norm and essential norm of differences of differentiation composition operators between Bloch spaces have been estimated in this paper. As a result, we find characterizations for boundedness and compactness of these operators.

Temperature variation intensively affects parameters of the friction force, particularly the average bristle deflections. In our earlier research work, a temperature dependent friction compensation scheme was developed for serial rigid robot manipulators which was comprised of a temperature dependent viscous friction compensation scheme and a temperature dependent disturbance rejection scheme. ...

In these lectures we discuss examples that are relevant to two questions in the theory of singular integrals. The first question is the L boundedness of the maximal operator formed by dilates of Mikhlin-Hörmander multipliers, while the second concerns the L boundedness of a well-known object, the classical L-bounded Calderón-Zygmund homogeneous singular integral associated with an integrable fu...

In this paper, we consider the commutators of fractional integrals ∫ Rd b(x)− b(y) |x− y| f(y)dy on the Sobolev spaces . H s p where b is a locally integrable function and r ∈ (0, d). We establish the equivalence between the boundedness of the commutators and the paraproducts of J.M. Bony. Then, we establish necessary and sufficient conditions for the boundedness of the paraproduit operator fro...