On pairs of unbounded self-adjoint operators satisfying an algebraic relation

Unbounded pairs of self-adjoint operatorsA andB satisfying the algebraic relationF ₁(A)B=BF ₂(A) are studied. For these relations, various definitions of integrable pairs of operators are presented and the class of tame relations is indicated; for the tame relations, the irreducible pairs are described and a structure theorem is presented.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 9, pp. 1253–1258, September, 1993.