On semibounded differential operators

The Trotter Product Formula for Perturbations of Semibounded Operators

On Semibounded Canonical Systems

We present two inverse spectral relations for canonical differential equations Jy′(x) = −zH(x)y(x), x ∈ [0, L): Denote by QH the TitchmarshWeyl coefficient associated with this equation. We show: If the Hamiltonian H is on some interval [0, ) of the form H(x) = „ v(x) v(x) v(x) 1 « , with a nondecreasing function v, then limx↘0 v(x) = limy→+∞QH(iy). If H is of the above form on some interval [l...

On Commuting Differential Operators

The theory of commuting linear differential expressions has received a lot of attention since Lax presented his description of the KdV hierarchy by Lax pairs (P,L). Gesztesy and the present author have established a relationship of this circle of ideas with the property that all solutions of the differential equations Ly = zy, z ∈ C, are meromorphic. In this paper this relationship is explored ...

Differential operators on orbifolds

An algorithm is presented that computes explicit generators for the ring of differential operators on an orbifold, the quotient of a complex vector space by a finite group action. The algorithm also describes the relations among these generators. The algorithm presented in this paper is based on Schwarz’s study of a map carrying invariant operators to operators on the orbifold and on an algorit...

Invariant Differential Operators On

For two positive integers m and n, we let Pn be the open convex cone in R consisting of positive definite n × n real symmetric matrices and let R be the set of all m×n real matrices. In this article, we investigate differential operators on the non-reductive manifold Pn × R (m,n) that are invariant under the natural action of the semidirect product group GL(n,R)⋉R on the MinkowskiEuclid space P...