Related papers: An asymptotic integral representation for Carleman…
Asymptotic expressions for Clebsch-Gordan coefficients are derived from an exact integral representation. Both the classically allowed and forbidden regions are analyzed. Higher-order approximations are calculated. These give, for example,…
The Ap\'ery polynomials and in particular their asymptotic behavior play an essential role in the understanding of the irrationality of \zeta(3). In this paper, we present a method to study the asymptotic behavior of the sequence of the…
Gegenbauer, also known as ultra-spherical polynomials appear often in numerical analysis or interpolation. In the present text we find a recursive formula and compute the asymptotic behavior for their $L^2$-norm.
The main aim of this short paper is to advertize the Koosis theorem in the mathematical community, especially among those who study orthogonal polynomials. We (try to) do this by proving a new theorem about asymptotics of orthogonal…
We establish the asymptotic zero distribution for polynomials generated by a four-term recurrence relation with varying recurrence coefficients having a particular limiting behavior. The proof is based on ratio asymptotics for these…
In this paper we consider the strong asymptotic behavior of Laguerre polynomials in the complex plane. The leading behavior is well known from Perron and Mehler-Heine formulas, but higher order coefficients, which are important in the…
We obtain uniform asymptotics for polynomials orthogonal on a fixed and varying arc of the unit circle with a positive analytic weight function. We also complete the proof of the large $s$ asymptotic expansion for the Fredholm determinant…
We study the asymptotic behavior of the ratio $|f(z)|/|z|$ as $z\to 0$ for mappings differentiable a.e. in the unit disc with non-degenerated Jacobian. The main tools involve the length-area functionals and angular dilatations depending on…
In the case when the weight and its inverse belong to BMO(T), we prove the asymptotics of the monic orthogonal polynomials in L^p, 2<p<p_0. Immediate applications include the estimates on the uniform norm and asymptotics for the polynomial…
The classical Painlev\'e equations are so well known that it may come as a surprise to learn that the asymptotic description of its solutions remains incomplete. The problem lies mainly with the description of families of solutions in the…
We study strong asymptotics of $L^r$-extremal polynomials for measures supported on Jordan regions with $C^{1+}$ boundary for $0<r<\infty$. Using the results for $r=2$, we derive asymptotics of weighted Chebyshev and residual polynomials…
This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting. For a wide class of compact, connected $C^\infty$ Riemannian manifolds, including the important cases of spheres and…
We compare the asymptotic behavior of Carmichael's lambda function composed with Euler's totient function to the asymptotic behavior of Carmichael's lambda function composed with itself. We establish the normal order of the logarithm of the…
The paper is devoted to the study of asymptotic behavior of solutions for nonlocal elliptic problems in weighted spaces. We deal with the most difficult case where the support of nonlocal terms intersects with the boundary of a plane…
A Gelfand-Tsetlin scheme of depth N is a triangular array with m integers at level m, m=1,...,N, subject to certain interlacing constraints. We study the ensemble of uniformly random Gelfand-Tsetlin schemes with arbitrary fixed N-th row. We…
Orthogonal polynomials on the unit circle are completely determined by their reflection coefficients through the Szeg\H{o} recurrences. We assume that the reflection coefficients converge to some complex number a with 0 < |a| < 1. The…
In this paper, we provide a complete Plancherel-Rotach asymptotic analysis of polynomials that satisfy a second-order difference equation with linear coefficients. According to the signs of the parameters, we classify the difference…
We prove that the Bergman kernel function associated to a smooth measure supported on a piecewise-smooth maximally totally real submanifold K in C^n is of polynomial growth (e.g, in dimension one, K is a finite union of transverse Jordan…
We investigate the asymptotic distribution of integrals of the $j$-function that are associated to ideal classes in a real quadratic field. To estimate the error term in our asymptotic formula, we prove a bound for sums of Kloosterman sums…
We study the uniform asymptotics for the orthogonal polynomials with respect to weights composed of both absolutely continuous measure and discrete measure, by taking a special class of the sieved Pollazek Polynomials as an example. The…