TY - JOUR

T1 - Differential operators on the algebra of densities and factorization of the generalized Sturm--Liouville operator

AU - Voronov, Theodore

AU - Shemyakova, Ekaterina

PY - 2018

Y1 - 2018

N2 - We consider factorization problem for differential operators on the commutative algebra of densities (defined either algebraically or in terms of an auxiliary extended manifold) introduced in 2004 by Khudaverdian and Voronov in connection with Batalin-Vilkovisky geometry. We consider the case of the line, where unlike the familiar setting (where operators act on functions) there are obstructions for factorization. We analyze these obstructions. In particular, we study the "generalized Sturm-Liouville" operators acting on the algebra of densities on the line. This in a certain sense is in between the 1D and 2D cases. We establish a criterion of factorizabily for the generalized Sturm-Liouville operator in terms of solution of the classical Sturm-Liouville equation. We also establish the possibility of an incomplete factorization.

AB - We consider factorization problem for differential operators on the commutative algebra of densities (defined either algebraically or in terms of an auxiliary extended manifold) introduced in 2004 by Khudaverdian and Voronov in connection with Batalin-Vilkovisky geometry. We consider the case of the line, where unlike the familiar setting (where operators act on functions) there are obstructions for factorization. We analyze these obstructions. In particular, we study the "generalized Sturm-Liouville" operators acting on the algebra of densities on the line. This in a certain sense is in between the 1D and 2D cases. We establish a criterion of factorizabily for the generalized Sturm-Liouville operator in terms of solution of the classical Sturm-Liouville equation. We also establish the possibility of an incomplete factorization.

U2 - 10.1007/s11005-018-1113-9

DO - 10.1007/s11005-018-1113-9

M3 - Article

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 1573-0530

ER -