Related papers: A note on bi-linear multipliers

We prove two conjectures of Shareshian and Wachs about Eulerian quasisymmetric functions and polynomials. The first states that the cycle type Eulerian quasisymmetric function $Q_{\lambda,j}$ is Schur-positive, and moreover that the…

Let $L$ be a homogeneous sublaplacian on a 2-step stratified Lie group $G$ of topological dimension $d$ and homogeneous dimension $Q$. By a theorem due to Christ and to Mauceri and Meda, an operator of the form $F(L)$ is bounded on $L^p$…

Let $\sigma(x,\xi) $ be a sufficiently regular function defined on $R^d \times R^d.$ The pseudo-differential operator with symbol $\sigma$ is defined on the Schwartz class by the formula: \[f\to\sigma f(x)=\int_{R^d} \sigma(x,\xi)…

In this short note, we consider bilinear pseudo-differential operators with symbols belonging to the Sj\"ostrand class. We show that those operators are bounded from the product of the $L^2$-based Sobolev spaces $H^{s_1} \times H^{s_2}$ to…

The main purpose of this paper is to introduce and investigate a class of generalized Bernoulli polynomials and Euler polynomials based on the generating function. we unify all forms of q-exponential functions by one more parameter. we…

Given an elliptic curve $E$ defined over $\mathbb{Q}$ which has potential complex multiplication by the ring of integers $\mathcal{O}_K$ of an imaginary quadratic field $K$ we construct a polynomial $P_E \in \mathbb{Z}[x,y]$ which is a…

Let $\mathbb{K}$ denote an algebraically closed field and let $V$ denote a vector space over $\mathbb{K}$ with finite positive dimension. Let $A,A^*$ denote a tridiagonal pair on $V$. We assume that $A,A^*$ belongs to a family of…

In this paper, we prove the existence of a bounded linear extension operator $T: L^{2,p}(E) \rightarrow L^{2,p}(\mathbb{R}^2)$ when $1<p<2$, where $E \subset \mathbb{R}^2$ is a certain discrete set with fractal structure. Our proof makes…

We consider the bilinear pseudo-differential operators with symbols in the bilinear H\"ormander classes $BS_{\rho, \rho}^m$, $0 < \rho < 1$. In this paper, we show that the condition $1/p = 1/p_1 + 1/p_2$ is necessary when we consider the…

A Schur multiplier is a linear map on matrices which acts on its entries by multiplication with some function, called the symbol. We consider idempotent Schur multipliers, whose symbols are indicator functions of smooth Euclidean domains.…

We prove that if $p \geq n^{-(q-6)/2}$, then asymptotically almost surely the binomial random $q$-uniform hypergraph $G^{(q)}(n,p)$ contains an $(n,q,2)$-Steiner system, provided $n$ satisfies the necessary divisibility conditions.

Let $ E=\{ (1, b_1, \ldots , b_n)\in R^{n+1} \mid \; b_i= \pm 1 ,\; i=1, \ldots, n \}$, $E^{\times n}_{\ne 0} := \{ W=(w_{i_1}, \ldots , w_{i_n}) \mid w_{i_k}\in E, \, k=1, \ldots, n, \, dim \, span(w_{i_1}, \ldots , w_{i_n}) = n \},$ and…

We show that if A is a set having small subtractive doubling in an abelian group, that is |A-A|< K|A|, then there is a polynomially large subset B of A-A so that the additive energy of B is large than (1/K)^{1 - \epsilon) where epsilon is a…

We prove the boundedness of a class of tri-linear operators consisting of a quasi piece of bilinear Hilbert transform whose scale equals to or dominates the scale of its linear counter part. Such type of operators is motivated by the…

We consider the quasi-periodic Jacobi operator $H_{x,\omega}$ in $l^2(\mathbb{Z})$ $(H_{x,\omega}\phi)(n) = -b(x+(n+1)\omega)\phi(n+1) - b(x+n\omega)\phi(n-1) + a(x+n\omega)\phi(n) = E\phi(n),\ n\in\mathbb{Z},$ where $a(x),\ b(x)$ are…

Bilinear pseudodifferential operators with symbols in the bilinear analog of all the H\"ormander classes are considered and the possibility of a symbolic calculus for the transposes of the operators in such classes is investigated. Precise…

A subset P of N x N is called Schur bounded if every infinite matrix with bounded entries which is zero off of P yields a bounded Schur multiplier on B(H). Such sets are characterized as being the union of a subset with at most k entries in…

Let $O(p,q)$ be the orthogonal groups of signature $(p,q)$ over the reals. It is shown that an element of the commutator subgroup $O(p,q)'$ of $O(p,q)$ is bireflectional (product of 2 involutions in $O(p,q)'$) if and only if it is…

In this paper, we establish the linear independence of values of the $q$-analogue of the exponential function, $E_q(x)$ and its derivatives at specified algebraic arguments, when $q$ is a Pisot-Vijayraghavan number. We also deduce similar…

We show that the binomial and related multiplicative character sums $$ \sum_{\stackrel{x=1}{(x,p)=1}}^{p^m} \chi (x^l(Ax^k +B)^w),\hspace{3ex} \sum_{x=1}^{p^m} \chi_1 (x)\chi_2(Ax^k +B), $$ have a simple evaluation for large enough $m$ (for…