Equivalence of Differential Operators

Some equivalence classes of operators on B(H)

On the Equivalence of Matrix Differential Operators to Schrödinger Form

We prove a generalization to the case of s × s matrix linear differential operators of the classical theorem of E. Cotton giving necessary and sufficient conditions for equivalence of eigenvalue problems for scalar linear differential operators. The conditions for equivalence to a matrix Schrödinger operator are derived and formulated geometrically in terms of vanishing conditions on the curvat...

The Beilinson Equivalence for Differential Operators and Lie Algebroids

Let D be the ring of differential operators on a smooth irreducible affine variety X over C; or, more generally, the enveloping algebra of any locally free Lie algebroid on X. The category of finitely-generated graded modules of the Rees algebra e D has a natural quotient category qgr( e D) which imitates the category of modules on Proj of a graded commutative ring. We show that the derived cat...

some equivalence classes of operators on b(h)

Equivalence operators in nilpotent systems