Related papers: On the numerical radius of the truncated adjoint S…

Given two arbitrary almost periodic functions with associated Fourier exponents which are linearly independent over the rational numbers, we prove that the existence of a common open vertical strip $V$, where both functions assume the same…

Let $\tau$ denote the divisor function, and $f$ be any multiplicative function that satisfies some mild hypotheses. We establish the asymptotic formula or non-trivial upper bound for the shifted convolution sum $\sum_{n \leq…

We present here several versions of the Grothendieck inequality over the skew field of quaternions: The first one is the standard Grothendieck inequality for rectangular matrices, and two additional inequalities for self-adjoint matrices,…

The affine connection in a space-time with a maximally symmetric spatial subspace is derived using the properties of maximally symmetric tensors. The number of degrees of freedom in metric-affine gravity is thereby considerably reduced…

Let $X_1,..., X_N\in\R^n$ be independent centered random vectors with log-concave distribution and with the identity as covariance matrix. We show that with overwhelming probability at least $1 - 3 \exp(-c\sqrt{n}\r)$ one has $ \sup_{x\in…

We mainly establish a monotonicity property between some special Riemann sums of a convex function $f$ on $[a,b]$, which in particular yields that $\frac{b-a}{n+1}\sum_{i=0}^n f\left(a+i\frac{b-a}{n}\right)$ is decreasing while…

Let $L$ be a linear differential operator with constant coefficients of order $n$ and complex eigenvalues $\lambda_{0},...,\lambda_{n}$. Assume that the set $U_{n}$ of all solutions of the equation $Lf=0$ is closed under complex…

We prove the existence of holomorphic functions $f$ defined on any open convex subset ${\rm \Omega}\subset {{\mathbb C}}^n$, whose partial sums of the Taylor developments approximate uniformly any complex polynomial on any convex compact…

Let T : Lp --> Lp be a contraction, with p strictly between 1 and infinity, and assume that T is analytic, that is, there exists a constant K such that n\norm{T^n-T^{n-1}} < K for any positive integer n. Under the assumption that T is…

Using a transference result, several inequalities of approximation by entire functions of exponential type in $\mathcal{C}(\mathbf{R})$, the class of bounded uniformly continuous functions defined on $\mathbf{R}:=\left( -\infty ,+\infty…

Let $\{a_n\}_1^\infty$ and $\{\theta_n\}_0^\infty$ be the sequences of partial quotients and approximation coefficients for the continued fraction expansion of an irrational number. We will provide a function $f$ such that $a_{n+1} =…

We derive constraints on the operator product expansion of two stress tensors in conformal field theories (CFTs), both generic and holographic. We point out that in large $N$ CFTs with a large gap to single-trace higher spin operators, the…

In this paper, we show several bounds for the numerical radius of a Hilbert space operator in terms of the Euclidean operator norm. The obtained forms will enable us to find interesting refinements of celebrated results in the literature.…

We introduce the non-commutative $f$-divergence functional $\Theta(\widetilde{A},\widetilde{B}):=\int_TB_t^{\frac{1}{2}}f\left(B_t^{-\frac{1}{2}} A_tB_t^{-\frac{1}{2}}\right)B_t^{\frac{1}{2}}d\mu(t)$ for an operator convex function $f$,…

We study the ring of all functions from the positive integers to some field. This ring, which we call \emph{the ring of number-theoretic functions}, is an inverse limit of the ``truncations'' \Gamma_n consisting of all functions f for which…

The purpose of this paper is to analysis the Harnack part of some truncated shifts whose $\rho$-numerical radius equal one in the finite dimensional case. As pointed out in Theorem 1.17 [12], a key point is to describe the null spaces of…

We identify subsets of the joint numerical range of an operator tuple in terms of its joint spectrum. This result helps us to transfer weak convergence of operator orbits into certain approximation and interpolation properties for powers in…

For a partition $\underline{\lambda} = (\lambda_{1}^{\rho _1}>\lambda_{2}^{\rho _2}>\lambda_{3}^{\rho _3}>\ldots>\lambda_{k}^{\rho _k})$ and its associated finite $\mathcal{R}$-module…

We return to Takagi's variational principle, generalized after forty years to two complex variables by Pfister. Both isolating some extremal rational functions associated to a bounded holomorphic function in the unit disk, respectively the…

We establish the \emph{inverse conjecture for the Gowers norm over finite fields}, which asserts (roughly speaking) that if a bounded function $f: V \to \C$ on a finite-dimensional vector space $V$ over a finite field $\F$ has large Gowers…