Related papers: Extremal norms for positive linear inclusions
In this work, the notions of normal cones at infinity to unbounded sets and limiting and singular subdifferentials at infinity for extended real value functions are introduced. Various calculus rules for these notions objects are…
Positive $C_0$-semigroups that occur in concrete applications are, more often than not, irreducible. Therefore a deep and extensive theory of irreducibility has been developed that includes characterizations, perturbation analysis, and…
This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These…
In this article, after recalling and discussing the conventional extremality, local extremality, stationarity and approximate stationarity properties of collections of sets and the corresponding (extended) extremal principle, we focus on…
The conventional definition of extremality of a finite collection of sets is extended by replacing a fixed point (extremal point) in the intersection of the sets by a collection of sequences of points in the individual sets with the…
Best possible bounds are established for families without s pairwise disjoint members and the more general problem for several families. The results are shown to apply several classical results.
This paper investigates the behavior of sets and functions at infinity by introducing new concepts, namely directional normal cones at infinity for unbounded sets, along with limiting and singular subdifferentials at infinity in the…
Uniform convergence rates are provided for asymptotic representations of sample extremes. These bounds which are universal in the sense that they do not depend on the extreme value index are meant to be extended to arbitrary samples…
We investigate the theory of finite observables, i.e., resolutions of the finite-dimensional identity by means of positive operators, that have a physical interpretation in terms of measurement schemes. We focus on extremal and rank-one…
An irreducible norm closed semigroup of complex matrices is simultaneously similar to a semigroup of partial isometries if and only if (a) the norms of all nonzero members of it are uniformly bounded above and below, and (b) its idempotents…
We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…
We extend the notions of "$R_\infty$-property" and "full (extended) Reidemeister spectrum" to finite groups in a meaningful way. We provide examples of finite groups admitting these properties, if they exist, by looking at groups of small…
All extremal solutions of the truncated $L$-problem of moments in two real variables , with support contained in a given compact set, are described as characteristic functions of semi-algebraic sets given by a single polynomial inequality.…
Compact-group representations on Banach spaces are known to be norm-continuous precisely when they have finite spectra. For a quantum group with continuous-function algebra $\mathcal{C}(\mathbb{G})$ norm continuity can be cast analogously…
We study the complex irreducible representations of special linear, symplectic, orthogonal and unitary groups over principal ideal local rings of length two. We construct a canonical correspondence between the irreducible representations of…
In this paper we introduce an enhanced notion of extremal systems for sets in locally convex topological vector spaces and obtain efficient conditions for set extremality in the convex case. Then we apply this machinery to deriving new…
We introduce and study some families of groups whose irreducible characters take values on quadratic extensions of the rationals. We focus mostly on a generalization of inverse semi-rational groups, which we call uniformly semi-rational…
The Hermitian eigenvalue problem asks for the possible eigenvalues of a sum of Hermitian matrices given the eigenvalues of the summands. This is a problem about the Lie algebra of the maximal compact subgroup of $G=\operatorname{SL}(n)$ .…
The joint spectral radius of a bounded set of $d \times d$ real matrices is defined to be the maximum possible exponential growth rate of products of matrices drawn from that set. For a fixed set of matrices, a sequence of matrices drawn…
Patterns on numerical semigroups are multivariate linear polynomials, and they are said to be admissible if there exists a numerical semigroup such that evaluated at any nonincreasing sequence of elements of the semigroup gives integers…