Related papers: Conditional positive definiteness as a bridge betw…

The curvature $\mathcal K_T(w)$ of a contraction $T$ in the Cowen-Douglas class $B_1(\mathbb D)$ is bounded above by the curvature $\mathcal K_{S^*}(w)$ of the backward shift operator. However, in general, an operator satisfying the…

Let $A_\infty ^+$ denote the class of one-sided Muckenhoupt weights, namely all the weights $w$ for which $\mathsf M^+:L^p(w)\to L^{p,\infty}(w)$ for some $p>1$, where $\mathsf M^+$ is the forward Hardy-Littlewood maximal operator. We show…

Let $0\leq \alpha<n$, $m\in \mathbb{N}$ and let consider $T_{\alpha,m}$ be a of integral operator, given by kernel of the form $$K(x,y)=k_1(x-A_1y)k_2(x-A_2y)\dots k_m(x-A_my),$$ where $A_i$ are invertible matrices and each $k_i$ satisfies…

Let $w$ denote a weight in $\mathbb{R}^n$ which belongs to the Muckenhoupt class $A_\infty$ and let $\mathsf{M}_w$ denote the uncentered Hardy-Littlewood maximal operator defined with respect to the measure $w(x)dx$. The \emph{sharp…

In this article we consider positivity issues for the clamped plate equation with high tension $\gamma>0$. This equation is given by $\Delta^2u - \gamma\Delta u=f$ under clamped boundary conditions. Here we show, that given a positive $f$,…

The study of entrywise powers of matrices was originated by Loewner in the pursuit of the Bieberbach conjecture. Since the work of FitzGerald and Horn (1977), it is known that $A^{\circ \alpha} := (a_{ij}^\alpha)$ is positive semidefinite…

The p-Laplace operator in the entire N-dimensional Euclidean space, subject to external electromagnetic potentials, is investigated. In the general case 1<p<N, the existence of at least one solution of mountain pass type to a weighted…

In this paper, we show a weighted Hardy inequality in a limiting case for functions in weighted Sobolev spaces with respect to an invariant measure. We also prove that the constant in the left-hand side of the inequality is optimal. As…

Let $L=-\Delta+V$ be a Schr\"odinger operator acting on $L^2(\mathbb R^n)$, $n\ge1$, where $V\not\equiv 0$ is a nonnegative locally integrable function on $\mathbb R^n$. In this paper, we first define molecules for weighted Hardy spaces…

The chiral susceptibility is given by the scalar vacuum polarisation at zero total momentum. This follows directly from the expression for the vacuum quark condensate so long as a nonperturbative symmetry preserving truncation scheme is…

This paper is concerned with orthonormal systems in real intervals, given with zero Dirichlet boundary conditions. More specifically, our interest is in systems with a skew-symmetric differentiation matrix (this excludes orthonormal…

We consider several types of quantum critical phenomena from finite-density gauge-gravity duality which to different degrees lie outside the Landau-Ginsburg-Wilson paradigm. These include: (1) a "bifurcating" critical point, for which the…

In this paper we attempt to lay the foundations for a theory encompassing some natural extensions of the class of subnormal operators, namely the $n$--subnormal operators and the sub-$n$--normal operators. We discuss inclusion relations…

Let $\Gamma $ be an infinite discrete group and $\mathsf{A}\subset \Gamma $ a nonempty finite subset. The set of permutations $\sigma $ of $\Gamma $ such that $s^{-1}\sigma (s)\in \mathsf{A}$ for every $s\in \Gamma $ can be identified with…

We characterize real and complex functions which, when applied entrywise to square matrices, yield a positive definite matrix if and only if the original matrix is positive definite. We refer to these transformations as sign preservers.…

Following the various statements of [DW16] to their logical conclusion, this note explicitly argues the following statement, implicit in [DW16]: for positive semi-definite operators $C_{1},\ldots,\,C_{L} $, a unitary $V_{C_{i}}$ commuting…

A surprising result of FitzGerald and Horn (1977) shows that $A^{\circ \alpha} := (a_{ij}^\alpha)$ is positive semidefinite (p.s.d.) for every entrywise nonnegative $n \times n$ p.s.d. matrix $A = (a_{ij})$ if and only if $\alpha$ is a…

For any bounded domain $\Omega$ in $\mathbb C^m,$ let ${\mathrm B}_1(\Omega)$ denote the Cowen-Douglas class of commuting $m$-tuples of bounded linear operators. For an $m$-tuple $\boldsymbol T$ in the Cowen-Douglas class ${\mathrm…

We study the stability of spinless Fermions with power law hopping $H_{ij} \propto |i - j|^{-\alpha}$. It is shown that at precisely $\alpha_c =2$, the dispersive inflection point coalesces with the band minimum and the charge carriers…

A classical theorem proved in 1942 by I.J. Schoenberg describes all real-valued functions that preserve positivity when applied entrywise to positive semidefinite matrices of arbitrary size; such functions are necessarily analytic with…