We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and periodic or antiperiodic boundary conditions. Then ...

It is well known that every Frobenius algebra is quasi-Frobenius, that is to say, if a finite dimensional algebra A over a field F has a nondegenerate bilinear form B such that B(xy, z) = B(x, yz) for all x, y, z ∊ A, then ...