Related papers: Asymptotics of a Class of Operator Determinants

In previous work the author found solutions to the Toda equations that were expressed in terms of determinants of integral operators. Here it is observed that a simple variant yields solutions to the matrix Toda equations. As an application…

We explicitly determine the high-energy asymptotics for Weyl-Titchmarsh matrices associated with general Dirac-type operators on half-lines and on $\bbR$. We also prove new local uniqueness results for Dirac-type operators in terms of…

The nonlinear recurrences we consider here include the functions $3x(1-x)$ and $\cos(x)$, which possess attractive fixed points $2/3$ and $0.739...$ (Dottie's number). Detailed asymptotics for oscillatory convergence are found, starting…

We consider the asymptotic properties of the Synthetic Control (SC) estimator when both the number of pre-treatment periods and control units are large. If potential outcomes follow a linear factor model, we provide conditions under which…

This article deals with the asymptotic behavior of fourth order differential equation where the coefficients are perturbations of linear constant coefficient equation. We introduce a change of variable and deduce that the new variable…

In this paper, ordinary and exponential dichotomies are defined in differential equations with equations with piecewise constant argument of general type. We prove the asymptotic equivalence between the bounded solutions of a linear system…

Let $D$ and $U$ be linear operators in a vector space (or more generally, elements of an associative algebra with a unit). We establish binomial-type identities for $D$ and $U$ assuming that either their commutator $[D,U]$ or the second…

We consider differential operators defined as Friedrichs extensions of quadratic forms with non-smooth coefficients. We prove a two term optimal asymptotic for the Riesz means of these operators and thereby also reprove an optimal Weyl law…

In this paper, we examine applications of the theory of operator-valued processes to algebraic methods in probability theory. We show a central limit theorem for general conservation operator processes. Utilizing this, we analyze the…

Sharp upper and lower estimates are obtained of the approximation numbers of a Sobolev embedding and an integral operator of Volterra type. These lead to asymptotic formulae for the approximation numbers and certain other s-numbers.

The quasiclassical asymptotics of the Knizhnik-Zamolodchikov equation with values in the tensor product of sl(2)- representations are considered. The first term of asymptotics is an eigenvector of a system of commuting operators. We show…

We establish new asymptotic results for the solutions of the second-grade fluids equations and characterize their decay rate in terms of the behavior of the initial data. Moreover, assuming more regularity for the initial data, we study the…

Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is…

We herein establish an asymptotic representation theorem for locally asymptotically normal quantum statistical models. This theorem enables us to study the asymptotic efficiency of quantum estimators such as quantum regular estimators and…

This paper is concerned with the asymptotic expansions of the amplitude of the solution of the Helmholtz equation. The original expansions were obtained using a pseudo-differential decomposition of the Dirichlet to Neumann operator. This…

We consider the linear relaxation Boltzmann equation in a semiclassical framework. We construct a family of sharp quasimodes for the associated operator which yields sharp spectral asymptotics for its small spectrum in the low temperature…

Asymptotic properties, both consistency and weak convergence, of estimators arising in a general class of dynamic recurrent event models are presented. The class of models take into account the impact of interventions after each event…

This paper is concerned with investigating the asymptotic behavior of the gradients of solutions to a class of elliptic systems with general boundary data, especially covering the Lam\'{e} systems, in a narrow region. The novelty of this…

In this paper, we prove asymptotic expansions of generalized partial theta functions with a nonprincipal Dirichlet character and relate these expansions to certain $L$-series.

We give a characterization of the compact operators on a model space in terms of asymptotic Toeplitz operators.