Spectral Asymptotics Revisited

Irregular Spectral Asymptotics

Asymptotics of Spectral Density Estimates

We consider nonparametric estimation of spectral densities of stationary processes, a fundamental problem in spectral analysis of time series. Under natural and easily verifiable conditions, we obtain consistency and asymptotic normality of spectral density estimates. Asymptotic distribution of maximum deviations of the spectral density estimates is also derived. The latter result sheds new lig...

Spectral asymptotics for canonical systems

Based on continuity properties of the de Branges correspondence, we develop a new approach to study the high-energy behavior of Weyl–Titchmarsh and spectral functions of 2×2 first order canonical systems. Our results improve several classical results and solve open problems posed by previous authors. Furthermore, they are applied to radial Dirac and radial Schrödinger operators as well as to Kr...

Spectral Asymptotics in Porous Media

This thesis consists of two papers devoted to the asymptotic analysis of eigenvalue problems in perforated domains. The first paper investigates by means of the two-scale convergence method the asymptotic behavior of eigenvalues and eigenfunctions of Stekloff eigenvalue problems in perforated domains. We prove a concise and precise homogenization result including convergence of gradients of eig...

Asymptotics of the Eulerian Numbers Revisited: a Large Deviation Analysis

Using the Saddle point method and multiseries expansions, we obtain from the generating function of the Eulerian numbers An,k and Cauchy’s integral formula, asymptotic results in non-central region. In the region k = n −nα, 1 >α> 1/2, we analyze the dependence of An,k on α. This paper fits within the framework of Analytic Combinatorics.