Related papers: An Extension of Young's Inequality
We develop a framework to extend resource measures from one domain to a larger one. We find that all extensions of resource measures are bounded between two quantities that we call the minimal and maximal extensions. We discuss various…
A generalization of Young's inequality for convolution with sharp constant is conjectured for scenarios where more than two functions are being convolved, and it is proven for certain parameter ranges. The conjecture would provide a unified…
The concept of measurability of functions on a charge space is generalised for functions taking values in a uniform space. Several existing forms of measurability generalise naturally in this context, and new forms of measurability are…
The Fenchel-Young inequality is fundamental in Convex Analysis and Optimization. It states that the difference between certain function values of two vectors and their inner product is nonnegative. Recently, Carlier introduced a very nice…
Two different sufficient conditions are given for the convergence of the Magnus expansion arising in the study of the linear differential equation $Y' = A(t) Y$. The first one provides a bound on the convergence domain based on the norm of…
In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical…
Similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.
We prove a homogenization result in terms of two-scale Young measures for non-local integral functionals. The result is obtained by means of a characterization of two-scale Young measures.
We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.
We investigate how basic probability inequalities can be extended to an imprecise framework, where (precise) probabilities and expectations are replaced by imprecise probabilities and lower/upper previsions. We focus on inequalities giving…
If a pair of functions nearly extremizes Young's convolution inequality for R^d, with all three exponents finite and strictly greater than 1, then each function is close in norm to a Gaussian. The proof relies on the Riesz-Sobolev…
The Simes inequality has received considerable attention recently because of its close connection to some important multiple hypothesis testing procedures. We revisit in this article an old result on this inequality to clarify and…
We study distributional similarity measures for the purpose of improving probability estimation for unseen cooccurrences. Our contributions are three-fold: an empirical comparison of a broad range of measures; a classification of similarity…
We have made some new definitions using the inequalities of Young' and Nesbitt'. And we have given some features of these new definitions. After, we established new Hadamard type inequalities for convex functions in the Young and Nesbitt…
We study finitely additive extensions of the asymptotic density to all the subsets of natural numbers. Such measures are called density measures. We consider a class of density measures constructed from free ultrafilters on $\mathbb{N}$ and…
In this work, we Extend Pawlak approximation spaces by topological spaces. Also, Rough Membership, equality and inclusion relations are extended using topological near open sets. In addition, new extended measures of accuracy and quality of…
Non-homogeneous self-similar measures are generically absolute continuous in the domain of parameters for which the similarity dimension is larger than one, see \cite{[SSS]}. Using certain algebraic curves we construct here exceptional…
We give variations on Ando's result comparing $f(B)-f(A)$ and $f(|B-A|)$ with respect to unitarily invariant norms on matrices.
In this short note, we give the refined Young inequality with Specht's ratio by only elementary and direct calculations. The obtained inequality is better than one previously shown by the author in 2012. In addition, we give a new property…
A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…