Related papers: Anti Lie-Trotter formula

We use topological ideas to show that, assuming the conjecture of Erd\"(o)s on subsets of positive integers having no $p$ terms in arithmetic progression (A. P.), there must exist a subset $M_p$ of positive integers with no $p$ terms in A.…

We show $L^p$ estimates for square roots of second order complex elliptic systems $L$ in divergence form on open sets in $\mathbb{R}^d$ subject to mixed boundary conditions. The underlying set is supposed to be locally uniform near the…

We prove that for a finite type curve in $\mathbb R^3$ the maximal operator generated by dilations is bounded on $L^p$ for sufficiently large $p$. We also show the endpoint $L^p \to L^{p}_{1/p}$ regularity result for the averaging operators…

Motivated by the study of trilinear forms for complex representations, we investigate the space of $G$-invariant linear forms on tensor products of irreducible admissible representations of $G = \mathrm{GL}_2(\mathbb{Q}_p)$ over…

In this paper the nonlinear matrix equation X-A^{*}X^{-p}A=Q with p>0 is investigated. We consider two cases of this equation: the case p>1 and the case 0<p<1. In the case p>1, a new sufficient condition for the existence of a unique…

Following Lang and Trotter we describe a probabilistic model that predicts the distribution of primes $p$ with given Frobenius traces at $p$ for two fixed elliptic curves over $\mathbb{Q}$. In addition, we propose explicit Euler product…

The radial probability measures on $R^p$ are in a one-to-one correspondence with probability measures on $[0,\infty[$ by taking images of measures w.r.t. the Euclidean norm mapping. For fixed $\nu\in M^1([0,\infty[)$ and each dimension p,…

In this note we consider a tent-like family with a cusp at the singular point and show that the linear response holds for certain perturbations of this family. This contrasts the tent-like maps with finite derivatives at the singularity.…

It is shown that, for any given $p\ge5$, $A>0$ and $B>0$, the exact upper bound on $\mathsf{E}|\sum X_i|^p$ over all independent zero-mean random variables (r.v.'s) $X_1,\ldots,X_n$ such that $\sum\mathsf{E}X_i^2=B$ and…

A $Z_2\times Z_2$-graded Lie superalgebra $g$ is a $Z_2\times Z_2$-graded algebra with a bracket $[.,.]$ that satisfies certain graded versions of the symmetry and Jacobi identity. In particular, despite the common terminology, $g$ is not a…

We obtain several generalizations the Hellinger theorem about $l^2$ solutions of difference equations: instead of second order equations and $ l^2$-solutions, we consider second-order equations with matrix coefficients and their solutions…

The $L_p$-discrepancy is a quantitative measure for the irregularity of distribution modulo one of infinite sequences. In 1986 Proinov proved for all $p>1$ a lower bound for the $L_p$-discrepancy of general infinite sequences in the…

We study the $L^{p},$ $1\leqslant p\leqslant \infty,$ boundedness for Riesz transforms of the form $V^{a}(-\frac{1}{2}\Delta+V)^{-a},$ where $a>0$ and $V$ is a non-negative potential. We prove that $V^{a}(-\frac{1}{2}\Delta+V)^{-a}$ is…

Let $\mathcal{B}$ be a nonempty homothecy invariant collection of convex sets of positive finite measure in $\mathbb{R}^2$. Let $M_\mathcal{B}$ be the geometric maximal operator defined by $$M_\mathcal{B}f(x) = \sup_{x \in R \in…

The Szeg\H{o} limit theorem by Fedele and Gebert for matrices of the type identity minus Hankel matrix is proved for the special case $1-\frac{\beta}{\pi}H_{N,\alpha}$ where $H_{N,\alpha}$ is the $N\times N$-Hilbert matrix,…

In a previous paper of the author, we establish a duality for the direct limit and the inverse limit of higher even $K$-groups over a $\mathbb{Z}_p^d$-extension. In this paper, we shall establish such a duality over certain non-commutative…

This paper proposes lower bounds on a quantity called $L^p$-norm joint spectral radius, or in short, $p$-radius, of a finite set of matrices. Despite its wide range of applications to, for example, stability analysis of switched linear…

We prove $L^p$ boundedness results, $p > 2$, for local maximal averaging operators over a smooth 2D hypersurface $S$ with either a $C^1$ density function or a density function with a singularity that grows as $|(x,y)|^{-\beta}$ for $\beta <…

Let $p$ be a prime and, for $A\subseteq \mathbb F_p$, define $A^\ast=(A+A)\cup(AA)$. S\'ark\"ozy conjectured that there exist constants $c>0$ and $p_0$ such that, for every prime $p>p_0$, every set $A\subseteq \mathbb F_p$ with…

We prove a compactness criterion for asymptotic $L_p$ spaces over arbitrary measure spaces. Total boundedness is characterized by almost equiboundedness together with total boundedness in $L_p$ of all truncations. This gives a…