On spectral asymptotics of the tensor product of operators with almost regular marginal asymptotics

Spectral Asymptotics of Laplace Operators on Surfaces with Cusps

Spectral Asymptotics for Schrödinger Operators with Periodic Point Interactions

Spectrum of the second-order differential operator with periodic point interactions in L2 R is investigated. Classes of unitary equivalent operators of this type are described. Spectral asymptotics for the whole family of periodic operators are calculated. It is proven that the first several terms in the asymptotics determine the class of equivalent operators uniquely. It is proven that the spe...

Spectral Asymptotics for Dirichlet Elliptic Operators with Non-smooth Coefficients

We consider a 2m-th-order elliptic operator of divergence form in a domain  of Rn, assuming that the coefficients are Hölder continuous of exponent r 2 (0, 1]. For the self-adjoint operator associated with the Dirichlet boundary condition we improve the asymptotic formula of the spectral function e( 2m , x , y) for x = y to obtain the remainder estimate O( n + dist(x , ) 1 n 1) with any 2 (0,...

On the Asymptotics of the Spectral Density of Radial Dirac Operators with Divergent Potential

The radial Dirac operator with a potential tending to infinity at infinity and satisfying a mild regularity condition is known to have a purely absolutely continuous spectrum covering the whole real line. Although having two singular end-points in the limit-point case, the operator has a simple spectrum and a generalised Fourier expansion in terms of a single solution. In the present paper, a s...

The Asymptotics of Almost Alternating Permutations

The goal of this paper is to study the asymptotic behavior of almost alternating permutations, that is, permutations that are alternating except for a finite number of exceptions. Let β l1 lk denote the number of permutations which consist of l1 ascents, l2 descents, l3 ascents, and so on. By combining the Viennot triangle and the boustrophedon transform, we obtain the exponential generating fu...