Related papers: The geometric mean is a Bernstein function
Using the convex functions in Grassmannian manifolds we can carry out interior estimates for mean curvature flow of higher codimension. In this way some of the results of Ecker-Huisken can be generalized to higher codimension
Recht and R\'{e} introduced the noncommutative arithmetic geometric mean inequality (NC-AGM) for matrices with a constant depending on the degree $d$ and the dimension $m$. In this paper we prove AGM inequalities with a dimension-free…
In this paper, we show that the $\nu$-weighted arithmetic mean is greater than the product of the $\nu$-weighted geometric mean and Specht's ratio. As a corollary, we also show that the $\nu$-weighted geometric mean is greater than the…
For two positive real numbers $x$ and $y$ let $H$, $G$, $A$ and $Q$ be the harmonic mean, the geometric mean, the arithmetic mean and the quadratic mean of $x$ and $y$, respectively. In this note, we prove that \begin{equation*} A\cdot G\ge…
We first show that hypergeometric functions appear naturally as spectral functions when applying pseudo-differential calculus to decipher heat kernel asymptotic in the situation where the symbol algebra is noncommutative. Such observation…
This paper deals with the famous isoperimetric inequality. In a first part, we give some new functional form of the isoperimetric inequality, and in a second part, we give a quantitative form with a remainder term involving Wasserstein…
[1] investigates advanced connotations of Hardy and Rellich-type inequalities on complete noncompact Riemannian manifolds, delving on deriving inequalities that incorporate poignant weight functions. These inequalities prolongate classical…
In order to study the analytic properties of the Goldbach generating function we consider a smooth version, similar to the Chebyshev function for the Prime Number Theorem. In this paper, we obtain explicit numerical estimates for the…
In this brief note, we show how to apply Kummer's and other quadratic transformation formulas for Gauss' and generalized hypergeometric functions in order to obtain transformation and summation formulas for series with harmonic numbers that…
In the paper [1] considered a new class of quaternionic mappings, so-called $G$-monogenic mappings. In this paper we prove analogues of classical integral theorems of the holomorphic function theory: the Cauchy integral theorems for surface…
The Riemannian metric on the manifold of positive definite matrices is defined by a kernel function $\phi$ in the form $K_D^\phi(H,K)=\sum_{i,j}\phi(\lambda_i,\lambda_j)^{-1} Tr P_iHP_jK$ when $\sum_i\lambda_iP_i$ is the spectral…
Motivated by the integral representation of the Euler Beta function, we introduce its Cauchy siblings and investigate some of their properties. Two of these newly introduced functions happen to coincide with some classical means, such as…
In this paper we construct a geometric analogue of the Weil representation over a finite field. Our construction is principally invariant, not choosing any specific realization. This eliminates most of the unpleasant formulas that appear in…
Two geometric inequalities are established for Einstein totally real submanifolds in a complex space form. As immediate applications of these inequalities, some non-existence results are obtained.
Generalized matrix-fractional (GMF) functions are a class of matrix support functions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix optimization problems associated with inverse problems,…
The main result says that every surjective isometry between two ideal Banach function spaces satisfying certain conditions can be presented as a composition of a measurable transformation of a variable and multiplication by a function.
A physically more adequate definition of a quaternionic holomorphic (H-holomorphic) function of one quaternionic variable compared to known ones and a quaternionic generalization of Cauchy-Riemann's equations are presented. At that a class…
We present an algorithm to compute the geometric median of shapes which is based on the extension of median to high dimensions. The median finding problem is formulated as an optimization over distances and it is solved directly using the…
The general Poisson summation formula of harmonic analysis and analytic number theory can be regarded as a quadrature formula with remainder. The purpose of this investigation is to give estimates for this remainder based on the classical…
We introduce and study the Steiner entire function, an analytic generating function for the intrinsic volumes of a convex compact set in a Hilbert space. This function extends the classical Steiner polynomial to infinite dimensions and…