Related papers: Bohnenblust--Hille inequality for cyclic groups

Some basic features of black-hole statistical mechanics are investigated, assuming that black holes respect the principles of quantum mechanics. Care is needed in defining an entropy S_bh corresponding to the number of microstates of a…

We investigate the conditions for a finite abelian group $G$ under which any cyclic subgroup $H$ and any group homomorphism $f \in \operatorname{Hom}(H,G)$ can be extended to an endomorphism $F \in \operatorname{End}(G)$. As a result, we…

We study the appearance of Hamilton $\ell$-cycles in dense $k$-uniform hypergraphs when $\ell \leq k-2$ and $k-\ell$ does not divide $k$. Our main result reduces this problem to the robust existence of a connected $\ell$-cycle tiling in…

At the Planck scale the distinction between elementary particles and black holes becomes fuzzy. The very definition of a "quantum black hole" (QBH) is an open issue. Starting from the idea that, at the Planck scale, the radius of the event…

The Doplicher-Haag-Roberts (DHR) reconstruction theorem shows that standard ($0$-form) internal symmetries are associated to groups in relativistic quantum field theory in spacetime dimension $D>2$. In particular, non-invertible symmetry…

For a Hilbert function space $\mathcal H$ the Smirnov class $\mathcal N^+(\mathcal H)$ is defined to be the set of functions expressible as a ratio of bounded multipliers of $\mathcal H$, whose denominator is cyclic for the action of…

The balanced hypercube $BH_{n}$, a variant of the hypercube, is a novel interconnection network for massive parallel systems. It is known that the balanced hypercube remains Hamiltonian after deleting at most $4n-5$ faulty edges if each…

In this note, among other results, we find the optimal constants of the generalized Bohnenblust--Hille inequality for $m$-linear forms over $\mathbb{R}$ and with multiple exponents $\left( 1,2,...,2\right) $, sometimes called mixed $\left(…

We provide a general sufficient condition for extendability of quasimorphisms on subgroups. This condition recovers the result of Hull--Osin on quasimorphisms on hyperbolically embedded subgroups, and the proof given in this paper is much…

For any $k\ge 3$ and $\ell \in [k-1]$ such that $(k,\ell) \ne (3,1)$, we show that any sufficiently large $k$-graph $G$ must contain a Hamilton $\ell$-cycle provided that it has no isolated vertices and every set of $k-1$ vertices contained…

We define the Heisenberg Kakeya maximal functions $M_{\delta}f$, $0<\delta<1$, by averaging over $\delta$-neighborhoods of horizontal unit line segments in the Heisenberg group $\mathbb{H}^1$ equipped with the Kor\'{a}nyi distance…

Recently, it has been shown by Ighachanea and Akkouchia \cite{0.1} that using binomial coefficients, one can derive some new refinements of Holder's inequalities. This inequalities then can be applied to a wide class of special functions…

The classical Bohr inequality states that if $ f $ is an analytic function with the power series representation $ f(z)=\sum_{n=0}^{\infty}a_nz^n $ in the unit disk $ \mathbb{D}:=\{z\in\mathbb{C} : |z|<1\} $ such that $ |f(z)|\leq 1 $ for…

Based on improving the classical Bohr inequality, we get in this paper some refined versions for a quasi-subordination family of functions, one of which is key to build our results. By means of these investigations, for a family of harmonic…

For $1\le d\le \ell< k$, we give a new lower bound for the minimum $d$-degree threshold that guarantees a Hamilton $\ell$-cycle in $k$-uniform hypergraphs. When $k\ge 4$ and $d< \ell=k-1$, this bound is larger than the conjectured minimum…

Let $k$ be a field of characteristic $0$, let $\mathsf{C}$ be a finite split category, let $\alpha$ be a 2-cocycle of $\mathsf{C}$ with values in the multiplicative group of $k$, and consider the resulting twisted category algebra…

Let G be a group and let A be the algebra of complex functions on G with finite support. The product in G gives rise to a coproduct on A making it a multiplier Hopf algebra. In fact, because there exist integrals, we get an algebraic…

We introduce the symmetric (respectively, non-symmetric) $\tau_{-\ell}-$hypergeometric functions associated with a root system of type $BC$ as joint eigenfunctions of a commutative algebra of differential (respectively,…

We generalize the classical Hardy and Faber-Krahn inequalities to arbitrary functions on a convex body $\Omega \subset \mathbb{R}^n$, not necessarily vanishing on the boundary $\partial \Omega$. This reduces the study of the Neumann…

For an algebra B with an action of a Hopf algebra H we establish the pairing between even equivariant cyclic cohomology and equivariant K-theory for B. We then extend this formalism to compact quantum group actions and show that equivariant…