Related papers: A Reverse Hilbert-like Optimal Inequality
We deal with the solution of a generic linear inverse problem in the Hilbert space setting. The exact right hand side is unknown and only accessible through discretised measurements corrupted by white noise with unknown arbitrary…
We propose a recursive algorithm for identifying all finite sequences of positive integers whose product equals their sum. Our method uses solutions of strictly shorter length that are iteratively extended in pursuit of a valid solution.…
We give a counterexample to a recently conjectured variant of the Penrose inequality.
The Hausdorff-Young inequality for Euclidean space, in its sharp form due to Beckner, gives an upper bound for the Fourier transform in terms of Lebesgue space norms, with an optimal constant. The extremizers have been identified by Lieb to…
In this paper, we show refined Young inequalities for two positive operators. Our results refine the ordering relations among the arithmetic mean, the geometric mean and the harmonic mean for two positive operators. In addition, we give two…
As a classic parameter from the binomial distribution, the binomial proportion has been well studied in the literature owing to its wide range of applications. In contrast, the reciprocal of the binomial proportion, also known as the…
This paper considers properties of an optimization based sampler for targeting the posterior distribution when the likelihood is intractable and auxiliary statistics are used to summarize information in the data. Our reverse sampler…
As a consequence of the Integral Test we find a triple inequality which bounds up and down both a series with respect to its corresponding improper integral, and reciprocally an improper integral with respect to its corresponding series.
The aim of this work is to improve Wilker inequalities near the origin and {\pi}/2.
We present a simple proof of the entropy-power inequality using an optimal transportation argument which takes the form of a simple change of variables. The same argument yields a reverse inequality involving a conditional differential…
We introduce a class of integral theorems based on cyclic functions and Riemann sums approximating integrals. The Fourier integral theorem, derived as a combination of a transform and inverse transform, arises as a special case. The…
We study the Riemannian quantiative isoperimetric inequality. We show that direct analogue of the Euclidean quantitative isoperimetric inequality is--in general--false on a closed Riemannian manifold. In spite of this, we show that the…
A stability version of the reverse isoperimetric inequality, and the corresponding inequality for isotropic measures are established.
We show that a certain conjectured optimal reverse Littlewood- Paley inequality would, if true, imply sharp results for the Kakeya maximal function, the Bochner-Riesz means and the Fourier restriction operator.
We prove a new inequality which improves on the classical Hardy inequality in the sense that a nonlinear integral quantity with super-quadratic growth, which is computed with respect to an inverse square weight, is controlled by the energy.…
This paper presents an inverse optimality method to solve the Hamilton-Jacobi-Bellman equation for a class of nonlinear problems for which the cost is quadratic and the dynamics are affine in the input. The method is inverse optimal because…
Using an inverse system of metric graphs as in: J. Cheeger and B. Kleiner, "Inverse limit spaces satisfying a Poincar\'e inequality", we provide a simple example of a metric space $X$ that admits Poincar\'e inequalities for a continuum of…
Let $h\geq 2$ and $A=\{a_0,a_1,\ldots,a_{k-1}\}$ be a finite set of integers. It is well-known that $\left|hA\right|=hk-h+1$ if and only if $A$ is a $k$-term arithmetic progression. In this paper, we give some nontrivial inverse results of…
In this paper, we study the norm-controlled inversion problem in two classes of algebras of integrable functions. In contrast of the classical case of $L^{1}(G)$, we prove that this problem has a positive solution in our setting without any…
We study the notion of reverse hypercontractivity. We show that reverse hypercontractive inequalities are implied by standard hypercontractive inequalities as well as by the modified log-Sobolev inequality. Our proof is based on a new…