Related papers: Hankel vector moment sequences and the non-tangent…

$H^2\zProd$ denotes the Hardy space of square integrable functions analytic in each variable separately. Let $P^{\ominus}$ be the natural projection of $L^2\zProd$ onto $\z8{H^2\zProd}$. A Hankel operator with symbol $b$ is the linear…

An appropriate rational approximation to the eigenfunction of the Schr\"{o}dinger equation for anharmonic oscillators enables one to obtain the eigenvalue accurately as the limit of a sequence of roots of Hankel determinants. The…

In this work we consider infinite dimensional extensions of some finite dimensional Gaussian geometric functionals called the Gaussian Minkowski functionals. These functionals appear as coefficients in the probability content of a tube…

Asymptotic expansion of a variation with anticipative weights is derived by the theory of asymptotic expansion for Skorohod integrals having a mixed normal limit. The expansion formula is expressed with the quasi-torsion, quasi-tangent and…

Recently, Wald and Henkel (2018) derived the leading-order estimate of the Humbert functions $\Phi_2$, $\Phi_3$ and $\Xi_2$ for two large arguments, but their technique cannot handle the Humbert function $\Psi_1$. In this paper, we…

It is well known that a non-constant complex-valued function $f$ defined on the open unit disk $\mathbb D$ is an analytic self-mapping of $\D$ if and only if Pick matrices $\left[…

We examine the asymptotic expansion of the Touchard polynomials $T_n(z)$ (also known as the exponential polynomials) for large $n$ and complex values of the variable $z$. In our treatment $|z|$ may be finite or allowed to be large like…

We aim to study Mittag-Leffler type functions of two variables ${{D}_{1}}\left( x,y \right),...,{{D}_{5}}\left( x,y \right)$ by analogy with the Appell hypergeometric functions of two variables. Moreover, we targeted functions…

Suppose $H$ is a finite dimensional reproducing kernel Hilbert space of functions on $X.$ If $H$ has the complete Pick property then there is an isometric map, $\Phi,$ from $X,$ with the metric induced by $H,$ into complex hyperbolic space,…

We establish the asymptotics of the joint moments of the characteristic polynomial of a random unitary matrix and its derivative for general real values of the exponents, proving a conjecture made by Hughes in 2001. Moreover, we give a…

Let $G_n$ be the Barnes multiple Gamma function of order $n$ and the function $f_n(z)$ be defined as \begin{align*} f_n(z)=\dfrac{\log G_n(z+1)}{z^n\Log z},\quad z\in \mathbb{C}\setminus (-\infty,0]. \end{align*} In this work, a conjecture…

The great success of the theory of hypergeometric series in one variable has stimulated the development of a corresponding theory in two and more variables. Horn has investigated the convergence of 34 (14 complete and 20 confluent)…

We find a relation guaranteeing that Hankel operators realized in the space of sequences $\ell^2 ({\Bbb Z}_{+}) $ and in the space of functions $L^2 ({\Bbb R}_{+}) $ are unitarily equivalent. This allows us to obtain exhaustive spectral…

For fixed size sampling designs with high entropy it is well known that the variance of the Horvitz-Thompson estimator can be approximated by the H\'ajek formula. The interest of this asymptotic variance approximation is that it only…

In this survey we show how to produce asymptotics of determinants of structured matrices using operator theory methods. We describe the asymptotics for finite Toeplitz matrices, finite Toeplitz plus Hankel matrices and generalizations of…

We study the asymptotic properties of monic orthogonal polynomials (OPs) with respect to some Freud weights when the degree of the polynomial tends to infinity, including the asymptotics of the recurrence coefficients, the nontrivial…

The Hamming graph $H(d,n)$ is the Cartesian product of $d$ complete graphs on $n$ vertices. Let $m=d(n-1)$ be the degree and $V = n^d$ be the number of vertices of $H(d,n)$. Let $p_c^{(d)}$ be the critical point for bond percolation on…

We study the asymptotic behavior of the Hopf characteristic function of fractals and chaotic dynamical systems in the limit of large argument. The small argument behavior is determined by the moments, since the characteristic function is…

Consider a branching random walk on $\mathbb Z$ in discrete time. Denote by $L_n(k)$ the number of particles at site $k\in\mathbb Z$ at time $n\in\mathbb N_0$. By the profile of the branching random walk (at time $n$) we mean the function…

We extend to multilinear Hankel operators the fact that truncation of bounded Hankel operators is bounded. We prove and use a continuity property of a kind of bilinear Hilbert transforms on product of Lipschitz spaces and Hardy spaces.