Search results for "Bounded"
showing 10 items of 658 documents
Representation of solutions and large-time behavior for fully nonlocal diffusion equations
2017
Abstract We study the Cauchy problem for a nonlocal heat equation, which is of fractional order both in space and time. We prove four main theorems: (i) a representation formula for classical solutions, (ii) a quantitative decay rate at which the solution tends to the fundamental solution, (iii) optimal L 2 -decay of mild solutions in all dimensions, (iv) L 2 -decay of weak solutions via energy methods. The first result relies on a delicate analysis of the definition of classical solutions. After proving the representation formula we carefully analyze the integral representation to obtain the quantitative decay rates of (ii). Next we use Fourier analysis techniques to obtain the optimal dec…
Adaptive backstepping based consensus tracking of uncertain nonlinear systems with event-triggered communication
2021
Abstract This paper investigates the consensus tracking problem for a class of uncertain high-order nonlinear systems with parametric uncertainties and event-triggered communication. Under a directed communication condition, a totally distributed adaptive backstepping based control scheme is presented. Specifically, a decentralized triggering condition is adopted in this paper such that continuous monitoring of neighboring states, as required in some existing results, can be avoided. Besides, to handle the non-differentiability problem of virtual controllers, which arises from the utilization of neighboring states collected only at the triggering instants, the virtual controllers in each re…
Approximation-based adaptive tracking control of stochastic nonlinear systems with a general form
2014
In this paper, an approximation-based adaptive tracking control scheme is proposed for a class of stochastic nonlinear systems with a more general structure. Fuzzy logical systems are used to approximate unknown nonlinearities in the controller design procedure and the backstepping technique is utilized to construct a state-feedback adaptive controller. The proposed controller can guarantee that all the signals in the closed-loop system are fourth-moment semi-globally uniformly ultimately bounded and the tracking error eventually converges to a small neighborhood around the origin. Simulation results are used to show the effectiveness of the proposed control scheme.
Marginal contribution, reciprocity and equity in segregated groups: Bounded rationality and selforganization in social networks
2007
We study the formation of social networks that are based on local interaction and simple rule following. Agents evaluate the profitability of link formation on the basis of the Myerson-Shapley principle that payoffs come from the marginal contribution they make to coalitions. The NP-hard problem associated with the Myerson-Shapley value is replaced by a boundedly rational 'spatially' myopic process. Agents consider payoffs from direct links with their neighbours (level 1), which can include indirect payoffs from neighbours' neighbours (level 2) and up to M-levels that are far from global. Agents dynamically break away from the neighbour to whom they make the least marginal contribution. Com…
Partial {$*$}-algebras of closable operators. I. The basic theory and the abelian case
1990
This paper, the first of two, is devoted to a systematic study of partial *-algebras of closable operators in a Hilbert space (partial Op*-algebras). After setting up the basic definitions, we describe canonical extensions of partial Op*-algebras by closure and introduce a new bounded commutant, called quasi-weak. We initiate a theory of abelian partial *-algebras. As an application, we analyze thoroughly the partial Op*-algebras generated by a single closed symmetric operator.
Sesquilinear forms associated to sequences on Hilbert spaces
2019
The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation theorems of sesquilinear forms, such as Kato's theorems. The associated operators correspond to classical frame operators or weakly-defined multipliers in the bounded context. In general some properties of them, such as the invertibility and the resolvent set, are related to properties of the sesquilinear forms. As an upshot of this approach new features of sequences (or pairs of sequences) which are semi-frames (or reproducing pairs) are obtained.
L∞ estimates in optimal mass transportation
2016
We show that in any complete metric space the probability measures μ with compact and connected support are the ones having the property that the optimal transportation distance to any other probability measure ν living on the support of μ is bounded below by a positive function of the L∞ transportation distance between μ and ν. The function giving the lower bound depends only on the lower bound of the μ-measures of balls centered at the support of μ and on the cost function used in the optimal transport. We obtain an essentially sharp form of this function. In the case of strictly convex cost functions we show that a similar estimate holds on the level of optimal transport plans if and onl…
Banach spaces of general Dirichlet series
2018
Abstract We study when the spaces of general Dirichlet series bounded on a half plane are Banach spaces, and show that some of those classes are isometrically isomorphic between themselves. In a precise way, let { λ n } be a strictly increasing sequence of positive real numbers such that lim n → ∞ λ n = ∞ . We denote by H ∞ ( λ n ) the complex normed space of all Dirichlet series D ( s ) = ∑ n b n λ n − s , which are convergent and bounded on the half plane [ Re s > 0 ] , endowed with the norm ‖ D ‖ ∞ = sup Re s > 0 | D ( s ) | . If (⁎) there exists q > 0 such that inf n ( λ n + 1 q − λ n q ) > 0 , then H ∞ ( λ n ) is a Banach space. Further, if there exists a strictly increasing sequ…
Interpolating sequences for bounded analytic functions
2007
. We prove that any sequence in the open ball of a complex Banach space E, even in that of E**, whose norms are an interpolating sequence for H∞, is interpolating for the space of all bounded analytic functions on BE-The construction made yields that the interpolating functions depend linearly on the interpolated values.
A bilinear version of Orlicz–Pettis theorem
2008
Abstract Given three Banach spaces X, Y and Z and a bounded bilinear map B : X × Y → Z , a sequence x = ( x n ) n ⊆ X is called B -absolutely summable if ∑ n = 1 ∞ ‖ B ( x n , y ) ‖ Z is finite for any y ∈ Y . Connections of this space with l weak 1 ( X ) are presented. A sequence x = ( x n ) n ⊆ X is called B -unconditionally summable if ∑ n = 1 ∞ | 〈 B ( x n , y ) , z ∗ 〉 | is finite for any y ∈ Y and z ∗ ∈ Z ∗ and for any M ⊆ N there exists x M ∈ X for which ∑ n ∈ M 〈 B ( x n , y ) , z ∗ 〉 = 〈 B ( x M , y ) , z ∗ 〉 for all y ∈ Y and z ∗ ∈ Z ∗ . A bilinear version of Orlicz–Pettis theorem is given in this setting and some applications are presented.