Search results for "Convex set"
showing 10 items of 35 documents
Shrinking and boundedly complete Schauder frames in Fréchet spaces
2014
We study Schauder frames in Fréchet spaces and their duals, as well as perturbation results. We define shrinking and boundedly complete Schauder frames on a locally convex space, study the duality of these two concepts and their relation with the reflexivity of the space. We characterize when an unconditional Schauder frame is shrinking or boundedly complete in terms of properties of the space. Several examples of concrete Schauder frames in function spaces are also presented.
Some regularity results on the ‘relativistic’ heat equation
2008
AbstractWe prove some partial regularity results for the entropy solution u of the so-called relativistic heat equation. In particular, under some assumptions on the initial condition u0, we prove that ut(t) is a Radon measure in RN. Moreover, if u0 is log-concave inside its support Ω, Ω being a convex set, then we show the solution u(t) is also log-concave in its support Ω(t). This implies its smoothness in Ω(t). In that case we can give a simpler characterization of the notion of entropy solution.
Robust control of continuous-time systems with state-dependent uncertainties and its application to electronic circuits
2014
In this paper, the problems of robust stability and stabilization are investigated for a class of continuous-time uncertain systems. The uncertainties in the model are state-dependent and belong to a polytopic convex set, as can be found in many electronic circuits and some other applications. The global asymptotic stability conditions for such systems are first established by the classic common quadratic Lyapunov function approach. To reduce conservativeness, a particular class of nonquadratic parameter-dependent Lyapunov functions is introduced, by which improved robust stability conditions for the underlying systems are also derived. Based on the stability criteria, a static output feedb…
Curves with no tritangent planes in space and their convex envelopes
1990
M. H. Freedman ([3]) proved that for a generic subset of closed curves in ~ 3 with nonvanishing curvature and torsion the number of t r i tangent planes is even and finite. He also guessed, for each even number s _> 0, the existence of an open subset A8 of closed curves with nonvanishing curvature and torsion such tha t each curve in A8 has exact ly s t r i t angent planes. A question tha t can be asked in this context is: Which curves with nonvanishing curvature and torsion have no t r i tangent planes? An example of such a curve is given by the (1,2)-curve on the torus with rat io a, 3 < a < 5 (see [2]). For a generi c curve, we give a pa r t i a l answer to this question here by finding …
A Birkhoff type integral and the Bourgain property in a locally convex space
2007
An integral, called the $Bk$-integral, for functions taking values in a locally convex space is defined. Properties of $Bk$-integrable functions are considered and the relations with other integrals are studied. Moreover the $Bk$-integrability of bounded functions is compared with the Bourgain property.
Bounds on the entanglement of two-qutrit systems from fixed marginals
2019
We discuss the problem of characterizing upper bounds on entanglement in a bipartite quantum system when only the reduced density matrices (marginals) are known. In particular, starting from the known two-qubit case, we propose a family of candidates for maximally entangled mixed states with respect to fixed marginals for two qutrits. These states are extremal in the convex set of two-qutrit states with fixed marginals. Moreover, it is shown that they are always quasidistillable. As a by-product we prove that any maximally correlated state that is quasidistillable must be pure. Our observations for two qutrits are supported by numerical analysis.
Some overdetermined problems related to the anisotropic capacity
2018
Abstract We characterize the Wulff shape of an anisotropic norm in terms of solutions to overdetermined problems for the Finsler p-capacity of a convex set Ω ⊂ R N , with 1 p N . In particular we show that if the Finsler p-capacitary potential u associated to Ω has two homothetic level sets then Ω is Wulff shape. Moreover, we show that the concavity exponent of u is q = − ( p − 1 ) / ( N − p ) if and only if Ω is Wulff shape.
Envelopes of open sets and extending holomorphic functions on dual Banach spaces
2010
We investigate certain envelopes of open sets in dual Banach spaces which are related to extending holomorphic functions. We give a variety of examples of absolutely convex sets showing that the extension is in many cases not possible. We also establish connections to the study of iterated weak* sequential closures of convex sets in the dual of separable spaces.
Robustness of the Gaussian concentration inequality and the Brunn–Minkowski inequality
2016
We provide a sharp quantitative version of the Gaussian concentration inequality: for every $r>0$, the difference between the measure of the $r$-enlargement of a given set and the $r$-enlargement of a half-space controls the square of the measure of the symmetric difference between the set and a suitable half-space. We also prove a similar estimate in the Euclidean setting for the enlargement with a general convex set. This is equivalent to the stability of the Brunn-Minkowski inequality for the Minkowski sum between a convex set and a generic one.
A Tomographical Characterization of L-convex Polyominoes
2005
Our main purpose is to characterize the class of L-convex polyominoes introduced in [3] by means of their horizontal and vertical projections. The achieved results allow an answer to one of the most relevant questions in tomography i.e. the uniqueness of discrete sets, with respect to their horizontal and vertical projections. In this paper, by giving a characterization of L-convex polyominoes, we investigate the connection between uniqueness property and unimodality of vectors of horizontal and vertical projections. In the last section we consider the continuum environment; we extend the definition of L-convex set, and we obtain some results analogous to those for the discrete case.