Converse mean value theorems on trees and symmetric spaces.
Convex concentration inequalities and forward-backward stochastic calculus.
Convex entropy decay via the Bochner–Bakry–Emery approach
We develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov processes in discrete settings. When this method applies the relative entropy decays in a convex way. The method is shown to be rather powerful when applied to a class of birth and death processes. We then consider other examples, including inhomogeneous zero-range processes and Bernoulli–Laplace models. For these two models, known results...
Convexity and almost convexity in groups
We give a review of results proved and published mostly in recent years, concerning real-valued convex functions as well as almost convex functions defined on a (not necessarily convex) subset of a group. Analogues of such classical results as the theorems of Jensen, Bernstein-Doetsch, Blumberg-Sierpiński, Ostrowski, and Mehdi are presented. A version of the Hahn-Banach theorem with a convex control function is proved, too. We also study some questions specific for the group setting, for instance...
Convexity inequalities for estimating generalized conditional entropies from below
Generalized entropic functionals are in an active area of research. Hence lower and upper bounds on these functionals are of interest. Lower bounds for estimating Rényi conditional -entropy and two kinds of non-extensive conditional -entropy are obtained. These bounds are expressed in terms of error probability of the standard decision and extend the inequalities known for the regular conditional entropy. The presented inequalities are mainly based on the convexity of some functions. In a certain...
Convexity with given infinite weight sequences.
Convex-like inequality, homogeneity, subadditivity, and a characterization of -norm
Let a and b be fixed real numbers such that 0 < mina,b < 1 < a + b. We prove that every function f:(0,∞) → ℝ satisfying f(as + bt) ≤ af(s) + bf(t), s,t > 0, and such that must be of the form f(t) = f(1)t, t > 0. This improves an earlier result in [5] where, in particular, f is assumed to be nonnegative. Some generalizations for functions defined on cones in linear spaces are given. We apply these results to give a new characterization of the -norm.
Correction Note to the Paper: On a Functional Equation Related to Families of Exponential Probability Measures
Correction to a paper by Newman and Sheingorn.
Correction to: An asymptotic form of Cauchy's functional equation; Volume 24, 2/3 (1982). (Short Communication).
Correction to "On a functional equation arising from hyperbolic geometry", Volume 21 (1980), 113-116.
Corrigendum to "Continuous solutions of a homogeneous functional equation".
Corrigendum to "Stability aspects of arithmetic functions, II" (Acta Arith. 139 (2009), 131-146)
Covering systems, Kubert identities and difference equations
Criteria for an exponential dichotomy of difference equations
Criteria for the Regularity of Continuous and Locally Integrable Solutions of a Class of Linear Functional Equations
Criterion of -criticality for one term -order difference operators
We investigate the criticality of the one term -order difference operators . We explicitly determine the recessive and the dominant system of solutions of the equation . Using their structure we prove a criticality criterion.
Curvature on a graph via its geometric spectrum
We approach the problem of defining curvature on a graph by attempting to attach a ‘best-fit polytope’ to each vertex, or more precisely what we refer to as a configured star. How this should be done depends upon the global structure of the graph which is reflected in its geometric spectrum. Mean curvature is the most natural curvature that arises in this context and corresponds to local liftings of the graph into a suitable Euclidean space. We discuss some examples.
Cyclic complex vector functional equations.