Determinants and Plemelj-Smithies formulas

Duván Cardona, Julio Delgado, Michael Ruzhansky

Published 2020-12-24Version 1

We establish Plemelj-Smithies formulas for classical Fredholm determinants by applying a recently introduced notion of invariant operators relative to a fixed decomposition of Hilbert spaces. The analysis also make use of the corresponding notion of full matrix-symbol. We also derive explicit formulas for determinants associated to elliptic operators on compact manifolds, compact Lie groups, and on homogeneous vector bundles over compact homogeneous manifolds.