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An integral formula for section determinants of semi-groups of linear operators. (English) Zbl 0995.47022

Summary: We derive an integral formula that expresses the section determinants of semigroups of linear operators through the solution to a linear integral equation. The solution theory of this integral equation is developedand for a special case a concrete solvability criterion is presented.

MSC:

47D06 One-parameter semigroups and linear evolution equations
47G10 Integral operators
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
47N20 Applications of operator theory to differential and integral equations
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