Related papers: Asymptotics of a Class of Operator Determinants

We define a class of discrete operators that, in particular, include the delta and nabla fractional operators.

We introduce and study {\it new} relative spectral invariants of {\it two} elliptic partial differential operators of Laplace and Dirac type on compact smooth manifolds without boundary that depend on both the eigenvalues and the…

We present a formula describing the asymptotics of a class of multivariate orthogonal polynomials with hyperoctahedral symmetry as the degree tends to infinity. The polynomials under consideration are characterized by a factorized weight…

We give an asymptotic formula for class numbers of orders in cubic number fields.

We prove an asymptotic bound on the eta invariant of a family of coupled Dirac operators on an odd dimensional manifold. In the case when the manifold is the unit circle bundle of a positive line bundle over a complex manifold, we obtain…

In this paper, we use basic asymptotic analysis to establish some uniform asymptotic formulas for the Fourier coefficients of the inverse of Jacobi theta functions. In particular, we answer and improve some problems suggested and…

We give a full set of Casimir operators for the symplectic group of arbitrary genus in terms of a basis chosen such that the action on representations of known $K$-type becomes transparent. We give examples for the latter.

Using the recent analysis of the output of the low-energy resolvent of Schr\"odinger operators on asymptotically conic manifolds (including Euclidean space) when the potential is short-range, we produce detailed asymptotic expansions for…

The present paper is mainly concerned with equations involving exponentials of bounded normal operators. Conditions implying commutativity of those normal operators are given. This is carried out without the known $2\pi i$-congruence-free…

We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction…

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…

We give asymptotic formulae for random matrix averages of derivatives of characteristic polynomials over the groups USp(2N), SO(2N) and O^-(2N). These averages are used to predict the asymptotic formulae for moments of derivatives of…

This contribution summarizes the results on the asymptotic performance of several variants of the FastICA algorithm. A number of new closed-form expressions are presented.

We study the asymptotic behavior of Multiple Meixner polynomials of first and second kind, respectively (see J. Arves\'u et al. J. Comput. Appl. Math., 153, (2003)). We use an algebraic function formulation for the solution of the…

The investigation of the asymptotic behavior of trigonometric series near the origin is a prominent topic in mathematical analysis. For trigonometric series in one variable, this problem was exhaustively studied by various authors in a…

We study asymptotical expansion as $\nu\to0$ for integrals over ${ \mathbb{R} }^{2d}=\{(x,y)\}$ of quotients of the form $F(x,y) \cos(\lambda x\cdot y) \big/ \big( (x\cdot y)^2+\nu^2\big)$, where $\lambda\ge 0$ and $F$ decays at infinity…

It is shown that every operator on (C[0,1]) which preserves a copy of an asymptotic (\ell_1) space, also preserves a copy of (C[0,1]).

In the present paper, firstly, we consider the Volterra integral equation of second type for a remainder term in an asymptotic formula of an arithmetic function which satisfies some special conditions and obtained a solution of the…

We deal with the asymptotic behaviour for $\lambda\to+\infty$ of the counting function $N_P(\lambda)$ of certain positive selfadjoint operators $P$ with double order $(m,\mu)$, $m,\mu>0$, $m\not=\mu$, defined on a manifold with ends $M$.…

Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear…