We derive an integral formula that expresses the section determinants of semi-groups of linear operators through the solution to a linear integral equation. The solution theory of this integral equation is developed and for a special case a concrete solvability criterion is presented.

Section determinants, semi-groups of linear operators, Green operators, linear integral equations, boundary value problems, unitary operators

47D06 (45P05 47A60 47N50 81Q05)