We study the notion of molecules in coorbit spaces. The main result states that if an operator, originally defined on an appropriate space of test functions, maps atoms to molecules, then it can be extended to a bounded operator on coorbit spaces. For time-frequency molecules we recover some boundedness results on modulation spaces, for time-scale molecules we obtain the boundedness on homogeno...

We prove the Lorentz-Shimogaki and Boyd theorems for the spaces Λu(w). As a consequence, we give the complete characterization of the strong boundedness of H on these spaces in terms of some geometric conditions on the weights u and w, whenever p > 1. For these values of p, we also give the complete solution of the weak-type boundedness of the Hardy-Littlewood operator on Λu(w).

The information boundedness principle for rule based inference process requires that the knowledge obtained as a result of a rule should not have more information than that contained in the consequent of this rule. We formulate the information boundedness principle for aggregation and show that it can be expressed using the notion of dominance. We also investigate conditions under which this pr...

Uniform boundedness, ultimate boundedness, uniform stability, and asymptotic stability are studied by analyzing a Liapunov function satisfying v′(t) ≤ −αv(t) + √ v(t) ∫ t # ω(t, s) √ v(s)ds, t ≥ t0 ≥ 0, (# = 0 or −∞). The results are then applied to integrodifferential equations x′(t) = A(t) [ x(t) + ∫ t # F (t, s)x(s)ds ] , t ≥ t0 ≥ 0, (# = 0 or −∞), in real Hilbert space with unbounded linear...

In this work we study the variational inequality problem in finite dimensional spaces. The constraint set we consider has the structure of semi-infinite programming. Standard convergence analysis for outer approximation methods includes boundedness of the constraint set, or, alternatively, coerciveness of the data. Using recession tools, we are able to replace these assumptions by the hypothese...

In this paper we will study the boundedness of all solutions for second-order differential equations ẍ+ f(x)ẋ+ λx+ g(x) = p(t), where λ ∈ R and g(x) satisfies the sublinear growth condition. Since the system in general is non-Hamiltonian, we have to introduce reversibility assumptions to apply the twist theorem for reversible mappings. Under some suitable conditions we then obtain the existence...

we present a two-dimensional continuous time dynamical system modeling a predatorprey food chain, and based on’s modified version of the Leslie-Gower scheme and on the Holling-type II scheme. The main result i$ given in terms of boundedness of solutions, existence of an attracting set and global stability of the coexisting interior equilibrium. @ 2003 Elsevier Ltd. All rights reserved. KeyWords...

We investigate the exponential turnpike property for finite horizon undiscounted discrete time optimal control problems without any terminal constraints. Considering a class of strictly dissipative systems we derive a boundedness condition for an auxiliary optimal value function which implies the exponential turnpike property. Two theorems illustrate how this boundedness condition can be conclu...

In this paper an analysis is provided of nonlinear monotonicity and boundedness properties for linear multistep methods. Instead of strict monotonicity for arbitrary starting values we shall focus on generalized monotonicity or boundedness with Runge-Kutta starting procedures. This allows many multistep methods of practical interest to be included in the theory. In a related manner, we also con...