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This paper studies properties of dual probabilistic frames -- in particular in relation to redundancy -- and introduces both approximately dual probabilistic frames and pseudo-dual probabilistic frames. We show that the canonical dual…
Given two $d\times d$ matrices, say $A$ and $B$, when do $p(A)$ and $p(B)$ have the same ``size'' for every polynomial $p$? In this article, we provide definitive results in the cases $d=2$ and $d=3$ when the notion of size used is the…
We show that any bounded domain in a doubling quasiconvex metric space can be approximated from inside and outside by uniform domains.
We consider a generalized Baernstein space associated to a compact family of finite subsets of an uncountable set. We show that for certain transfinitely defined families such spaces admit an equivalent $2$-rotund norm. We also show that…
In this paper, ordinary and exponential dichotomies are defined in differential equations with equations with piecewise constant argument of general type. We prove the asymptotic equivalence between the bounded solutions of a linear system…
I explain the difficulty of making various concepts of and relating to probability precise, rigorous and physically significant when attempting to apply them in reasoning about objects (e.g., spacetimes) living in infinite-dimensional…
Minimizing divergence measures under a constraint is an important problem. We derive a sufficient condition that binary divergence measures provide lower bounds for symmetric divergence measures under a given triangular discrimination or…
A d.c. (delta-convex) function on a normed linear space is a function representable as a difference of two continuous convex functions. We show that an infinite dimensional analogue of Hartman's theorem on stability of d.c. functions under…
We classify the metric spaces that can be approximated by finite homogeneous ones.
This paper investigates sufficient and necessary conditions for the existence of a homotopy equivalence between two finite simplicial complexes from an algorithmic point of view. As a result, the conditions are formulated in terms of the…
Two-weight norm estimates for the double Hardy transforms and strong fractional maximal functions are established in variable exponent Lebesgue spaces. Derived conditions are simultaneously necessary and sufficient in the case when the…
Hardy spaces in the complex plane and in higher dimensions have natural finite-dimensional subspaces formed by polynomials or by linear maps. We use the restriction of Hardy norms to such subspaces to describe the set of possible…
We study the asymmetry of the Lipschitz metric d on Outer space. We introduce an (asymmetric) Finsler norm that induces d. There is an Out(F_n)-invariant potential \Psi on Outer space such that when the Lipschitz norm is corrected by the…
We show that no matter what subset of a normed space is given, a typical 1-Lipschitz mapping into a Banach space is non-differentiable at a typical point of the set in a very strong sense: the derivative ratio approximates, on arbitrary…
We show that there exist infinite-dimensional extremely non-complex Banach spaces, i.e. spaces $X$ such that the norm equality $\|Id + T^2\|=1 + \|T^2\|$ holds for every bounded linear operator $T:X\longrightarrow X$. This answers in the…
We answer the question: "on which metric spaces $(M,d)$ are all continuous functions uniformly continuous?" Our characterization theorem improves and generalizes a previous result due to Levine and Saunders, and in particular is applicable…
Two different notions of {\mu}-equicontinuity that apply to topological dynamical systems and probability measures were studied by Gilman (1987) and Huang-Lu-Ye (2011). One was used to classify measure preserving topological dynamical…
Plausibility measures are structures for reasoning in the face of uncertainty that generalize probabilities, unifying them with weaker structures like possibility measures and comparative probability relations. So far, the theory of…
We establish the equivalence of the analytic and probabilistic notions of subharmonicity in the framework of general symmetric Hunt processes on locally compact separable metric spaces, extending an earlier work of the first named author on…
In this paper we propose a definition of regularity suited for polar spaces of infinite rank and we investigate to which extent properties of regular polar spaces of finite rank can be generalized to polar spaces of infinite rank.