相关论文: Asymptotics for Toeplitz determinants on a circula…

In this note we discuss an open problem whether a truncated Toeplitz operator on a model space can be hypercyclic. We compute point spectrum and eigenfunctions for a class of truncated Toeplitz operators with polynomial analytic and…

In 1975 K. Michael Day produced an exact formula for the determinants of finite Toeplitz matrices whose symbols are rational. The answer is a sum that involves powers of the roots of the numerator of the symbol and whose coefficients depend…

In this paper, we are concerned with the asymptotic behavior of weak solutions to certain elliptic and parabolic problems involving the fractional $p$-Laplacian in cylindrical domains that become unbounded in one direction. The nonlocal…

Several asymptotic expansions and formulas for cubic exponential sums are derived. The expansions are most useful when the cubic coefficient is in a restricted range. This generalizes previous results in the quadratic case and helps to…

Problems in exponential asymptotics are typically characterized by divergence of the associated asymptotic expansion in the form of a factorial divided by a power. In this paper, we demonstrate that in certain classes of problems that…

We study the questions of determining the asymptotics of the probabilistic characteristics of additive arithmetic functions in the paper, regardless of whether they have a limit distribution or not. Several assertions are proved about the…

In this paper we give an asymptotic of the coefficients of the orthogonal polynomials on the unit circle, with respect of a weight of type $\displaystyle{ f : \theta \mapsto \prod_{1\le j \le M} \vert 1 - e^{i(\theta_{j}-\theta)}\vert…

We describe the asymptotic behavior of the mapping function at an analytic cusp compared with Kaiser's results for cusps with small perturbation of angles and the known explicit formulae for cusps with circular boundary curves. We propose a…

We use Toeplitz operators to define a star-product on Poisson manifolds whose Poisson structure is induced by a symplectic Lie algebroid. The Toeplitz operators we consider are defined on groupoids whose algebroid can be endowed with a…

The explicit formula for the hyperbolic metric $\lambda_{\alpha,\,\beta,\,\gamma}(z)|dz|$ on the thrice-punctured sphere $\mathbb{P} \backslash \{z_1,\,z_2,\,z_3\}$ with singularities of order $\alpha,\,\beta,\,\gamma \leq 1$ with…

We study the asymptotic behavior of extremal length along Teichm\"uller rays. Specifically, we determine the limit of extremal length along a Teichm\"uller ray and obtain an explicit expression for this limit, which complements a related…

Let F be the quotient of an analytic function with a product of linear functions. Working in the framework of analytic combinatorics in several variables, we compute asymptotic formulae for the Taylor coefficients of F using multivariate…

In this paper we study the asymptotic behavior of solutions to an elliptic equation near the singularity of an inverse square potential with a coefficient related to the best constant for the Hardy inequality. Due to the presence of a…

We prove the existence of non-decaying real solutions of the Johnson equation, vanishing as $x\to+\infty$. We obtain asymptotic formulas as $t\to\infty$ for the solutions in the form of an infinite series of asymptotic solitons with curved…

We compute an asymptotic formula for the supremum of the resolvent norm ($\zeta$ -T ) -1 over |$\zeta$| $\ge$ 1 and contractions T acting on an n-dimensional Hilbert space, whose spectral radius does not exceed a given r $\in$ (0, 1). We…

The well-known asymptotic formula for the module of a condenser with one of the plates degenerating to a point is generalized to the case of a condenser of general type. The condensers under consideration consist of n plates, n > 2, and the…

We classify the local asymptotic behavior of positive singular solutions to a class of subcritical sixth order equations on the punctured ball. Initially, using a version of the integral moving spheres technique, we prove that solutions are…

We derive a two-terms asymptotics for eigenvalues of the Dirichlet Laplacian in a narrow strip of variable width. The asymptotics is taken with respect to a small paprameter that characterizes the width of the strip.

We determine the asymptotic behavior of twisted traces of singular moduli with a power-saving error term in both the discriminant and the order of the pole at $i\infty$. Using this asymptotic formula, we obtain an exact formula for these…

We show that the spectrum of the open-boundary limit of banded Toeplitz matrices is real whenever the associated symbol function is real-valued along a closed polar curve. Building on this result, we develop both analytical and numerical…