Search results for "Bounded"
showing 10 items of 658 documents
A Lebesgue-type decomposition on one side for sesquilinear forms
2021
Sesquilinear forms which are not necessarily positive may have a dierent behavior, with respect to a positive form, on each side. For this reason a Lebesgue-type decomposition on one side is provided for generic forms satisfying a boundedness condition.
Coherent Conditional Previsions and Proper Scoring Rules
2012
In this paper we study the relationship between the notion of coherence for conditional prevision assessments on a family of finite conditional random quantities and the notion of admissibility with respect to bounded strictly proper scoring rules. Our work extends recent results given by the last two authors of this paper on the equivalence between coherence and admissibility for conditional probability assessments. In order to prove that admissibility implies coherence a key role is played by the notion of Bregman divergence.
Observer-based finite-time fuzzy H∞ control for discrete-time systems with stochastic jumps and time-delays
2014
This paper is concerned with the problem of observer-based finite-time H ∞ control for a family of discrete-time Markovian jump nonlinear systems with time-delays represented by Takagi-Sugeno (T-S) model. The main contribution of this paper is to design an observer-based finite-time H ∞ controller such that the resulting closed-loop system is stochastic finite-time bounded and satisfies a prescribed H ∞ disturbance attenuation level over the given finite-time interval. Sufficient criteria on stochastic finite-time H ∞ stabilization via observer-based fuzzy state feedback are presented for the solvability of the problem, which can be tackled by a feasibility problem in terms of linear matrix…
Collision Orbits in the Isosceles Rectilinear Restricted Problem
1995
In the study of the Collinear Three-Body Problem, McGehee (1974) introduced a new set of coordinates which had the effect of blowing up the triple collision singularity. Subsequently, his method has been used to analyze some other collision or singularities. Recently, Wang (1986) introduced another transformation which differs from the McGehee’s coordinates in the fact that the blowing-up factor is now the potential function, U, instead of the moment of inertia, I. Meyer and Wang (1993) have applied this method to the Restricted Isosceles Three-body Problem with positive energy and Cors and Llibre (1994) to the hyperbolic restricted three-body problem. In this paper we study the singulariti…
Further results on H<inf>&#x221E;</inf> control of switched linear time-delay systems
2012
In this note, we study the problems of stability analysis and H ∞ controller synthesis of discrete-time switched systems with time-varying delay. The system under consideration is firstly transformed into an interconnection system. Based on the system transformation and the scaled small gain theorem, the asymptotic stability of the original system is examined via the version of the bounded realness of the transformed forward system. The aim of the proposed approach is to reduce conservatism, which is made possible by a precise approximation of the time-varying delay and the input-output approach. The proposed stability condition is demonstrated to be much less conservative than most existin…
Boundedness and spectral invariance for standard pseudodifferential operators on anisotropically weighted LP-Sobolev spaces
1990
It is shown that pseudodifferential operators with symbols in the standard classes S ρ,δ m (ℝn) define bounded maps between large classes of weighted LP-Sobolev spaces where the growth of the weight does not have to be isotropic. Moreover, the spectrum is independent of the choice of the space.
Maximal potentials, maximal singular integrals, and the spherical maximal function
2014
We introduce a notion of maximal potentials and we prove that they form bounded operators from L to the homogeneous Sobolev space Ẇ 1,p for all n/(n − 1) < p < n. We apply this result to the problem of boundedness of the spherical maximal operator in Sobolev spaces.
Regularity of the Inverse of a Sobolev Homeomorphism
2011
We give necessary and sufficient conditions for the inverse ofa Sobolev homeomorphism to be a Sobolev homeomorphism and conditions under which the inverse is of bounded variation.
Uniform, Sobolev extension and quasiconformal circle domains
1991
This paper contributes to the theory of uniform domains and Sobolev extension domains. We present new features of these domains and exhibit numerous relations among them. We examine two types of Sobolev extension domains, demonstrate their equivalence for bounded domains and generalize known sufficient geometric conditions for them. We observe that in the plane essentially all of these domains possess the trait that there is a quasiconformal self-homeomorphism of the extended plane which maps a given domain conformally onto a circle domain. We establish a geometric condition enjoyed by these plane domains which characterizes them among all quasicircle domains having no large and no small bo…
APPROXIMATION OF BANACH SPACE VALUED NON-ABSOLUTELY INTEGRABLE FUNCTIONS BY STEP FUNCTIONS
2008
AbstractThe approximation of Banach space valued non-absolutely integrable functions by step functions is studied. It is proved that a Henstock integrable function can be approximated by a sequence of step functions in the Alexiewicz norm, while a Henstock–Kurzweil–Pettis and a Denjoy–Khintchine–Pettis integrable function can be only scalarly approximated in the Alexiewicz norm by a sequence of step functions. In case of Henstock–Kurzweil–Pettis and Denjoy–Khintchine–Pettis integrals the full approximation can be done if and only if the range of the integral is norm relatively compact.