Related papers: Strong asymptotics for Christoffel functions of pl…
We fully determine a uniformly valid asymptotic behaviour for large $a \omega$ and fixed $m$ of the angular solutions and eigenvalues of the spin-weighted spheroidal differential equation. We fully complement the analytic work with a…
We prove the asymptotic formulas for the transition densities of isotropic unimodal convolution semigroups of probability measures on $\mathbb{R} ^d$ under the assumption that its L\'{e}vy--Khintchine exponent varies slowly. We also derive…
The spin-weighted spheroidal eigenvalues and eigenfunctions arise in the separation by variables of spin-field perturbations of Kerr black holes. We derive a large, real-frequency asymptotic expansion of the spin-weighted spheroidal…
In this paper we establish a close connection between three notions at- tached to a modular subgroup. Namely the set of weight two meromorphic modular forms, the set of equivariant functions on the upper half-plane commuting with the action…
Bessel and modified Bessel functions of imaginary order $i\nu$ ($\nu >0$) are studied. Asymptotic expansions are derived as $\nu \to \infty$ that are uniformly valid in unbounded complex domains, with error bounds provided. Coupled with…
We study the leading coefficient in the asymptotical formula $ N (R) = \frac{W}{\pi} R + O (1) $, $ R \to \infty $, for the resonance counting function $ N (R)$ of Schr\"odinger Hamiltonians with point interactions. For such Hamiltonians,…
For a system of two measures supported on a starlike set in the complex plane, we study asymptotic properties of associated multiple orthogonal polynomials $Q_{n}$ and their recurrence coefficients. These measures are assumed to form a…
We study right limits of the Bergman Shift matrix. Our results have applications to ratio asymptotics, weak asymptotic measures, relative asymptotics, and zero counting measures of the orthogonal and orthonormal polynomials.
Uniform asymptotic expansions are derived for reverse generalised Bessel polynomials of large degree $n$, real parameter $a$, and complex argument $z$, which are simpler than previously known results. The defining differential equation is…
We prove fractional Leibniz rules and related commutator estimates in the settings of weighted and variable Lebesgue spaces. Our main tools are uniform weighted estimates for sequences of square-function-type operators and a bilinear…
We show that the Christoffel function (CF) factorizes (or can be disintegrated) as the product of two Christoffel functions, one associated with the marginal and the another related to the conditional distribution, in the spirit of "the CF…
The purpose of the present paper is to give unified expressions to the characteristic functions of all elliptical and related distributions. Those distributions including the multivariate elliptical symmetric distributions and some…
For a polarized algebraic manifold $(X,L)$, let $T$ be an algebraic torus in the group of all holomorphic automorphisms of $X$. Then strong relative K-stability will be shown to imply asymptotic relative Chow-stability. In particular, by…
For the multi-sample equal covariance function (ECF) testing problem, Zhang (2013) proposed an $L^{2}$-norm based test. However, its asymptotic power and finite sample performance have not been studied. In this paper, its asymptotic power…
Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing \cite{GSE}, we derive asymptotics for…
We establish asymptotic estimates of Mathieu-type series defined by sequences with power-logarithmic or factorial behavior. By taking the Mellin transform, the problem is mapped to the singular behavior of certain Dirichlet series, which is…
By exploiting a variational technique based upon projecting over the Pohozaev manifold, we prove existence of positive solutions for a class of nonlinear fractional Schrodinger equations having a nonhomogenous nonautonomous asymptotically…
In this work we study the Plancherel-Rotach type asymptotics for $q$-Laguerre orthogonal polynomials with complex scaling . The main term of the asymptotics contains Ramanujan function $A_{q}(z)$ for the scaling parameter on the vertical…
This paper concerns an analytic and numerical analysis of a class of weighted singular Cauchy integrals with exponential weights $w:=\exp(-Q)$ with finite moments and with smooth external fields $Q:\mathbb R\to [0,\infty)$, with varying…
In this work we investigate the asymptotics for Euler's $q$-Exponential $E_{q}(z)$, $q$-Gamma function $\Gamma_{q}(z)$, Ramanujan's function $A_{q}(z)$, Jackson's $q$-Bessel function $J_{\nu}^{(2)}$(z;q) of second kind, Stieltjes-Wigert…