Related papers: Reverse Triangle Inequalities for Potentials
Computation of polynomial relative invariants is a classical tool in algebra. Relative differential invariants are central for the equivalence problem of geometric structures. We address the fundamental problem of finite generation of their…
Reverse H\"{o}lder inequalities for a class of functions on a probability space constitute an important tool in Analysis in Probability. After revisiting how a (modified) log-Sobolev inequality can be used to derive reverse H\"{o}lder…
In this paper, we provide explicit formulas for the exact inverses of the symmetric tridiagonal near-Toeplitz matrices characterized by weak diagonal dominance in the Toeplitz part. Furthermore, these findings extend to scenarios where the…
For a closed connected surface with a metric g, we consider the regularized trace of the inverse of the Laplace-Beltrami operator. We minimize this on the class of smooth metrics conformal to g having the same area, and show that the…
We prove two new reverse Cauchy--Schwarz inequalities of additive and multiplicative types in a space equipped with a positive sesquilinear form with values in a C*-algebra. We apply our results to get some norm and integral inequalities.…
In this paper, we study a new type of inverse problem on warped product Riemannian manifolds with connected boundary that we name warped balls. Using the symmetry of the geometry, we first define the set of Regge poles as the poles of the…
This work concerns the distance in 2-norm from a matrix polynomial to a nearest polynomial with a specified number of its eigenvalues at specified locations in the complex plane. Perturbations are allowed only on the constant coefficient…
The paper considers a multidimensional problem of optimal recovery of an operator whose action is represented by multiplying the original function by a weight function of a special type, based on inaccurately specified information about the…
We study the mixed Dirichlet-Neumann problem for the Laplace equation in the complement of a bounded convex polygonal quadrilateral in the extended complex plane. The Dirichlet\,/\,Neumann conditions at opposite pairs of sides are $\{0,1\}$…
The aim of this paper is to obtain some generalized weighted Ostrowski inequalities for differentiable mappings. Some well known inequalities can be derived as special cases of the inequalities obtained here. In addition, perturbed…
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…
We study an inverse resonance problem on the line in which we aim at determining a compactly supported and integrable perturbation of a fixed P\"oschl-Teller potential. We define the resonances as the poles of the reflection coefficients…
We examine a number of known inequalities for $L^p$ functions with reverse representations for $s<1$ with complex matrices under the $p$-norms $||X||_p=\text{Tr}[(X^\ast X)^{p/2}]^{1/p}$, and similarly defined quasinorm or antinorm…
In this manuscript, we analyze the expansions of functions in orthogonal polynomials associated with a general weight function in a multidimensional setting. Such orthogonal polynomials can be obtained by Gram-Schmidt orthogonalization.…
Sharp extensions of Pitt's inequality and bounds for Stein-Weiss fractional integrals are obtained that incorporate gradient forms and vector-valued operators. Such results include Hardy-Rellich inequalities.
We establish a new global endpoint Sobolev inequality for measures that extends the classical theorem of Meyers-Ziemer by placing a maximal function on the right-hand side. This result has several significant consequences. It extends…
Weighted cone-volume functionals are introduced for the convex polytopes in $\mathbb{R}^n$. For these functionals, geometric inequalities are proved and the equality conditions are characterized. A variety of corollaries are derived,…
We consider random orthonormal polynomials $$ P_{n}(x)=\sum_{i=0}^{n}\xi_{i}p_{i}(x), $$ where $\xi_{0}$, . . . , $\xi_{n}$ are independent random variables with zero mean, unit variance and uniformly bounded $(2+\ep_0)$-moments, and…
A geometric inequality among three triangles, originating in circle packing problems, is introduced. In order to prove it, we reduce the original formulation to the nonnegativity of a particular polynomial in four real indeterminates.…
We solve a class of isoperimetric problems on $\mathbb{R}^N $ with respect to weights that are powers of the distance to the origin. For instance we show that if $k\in [0,1]$, then among all smooth sets $\Omega$ in $\mathbb{R} ^N$ with…