Geodesic
Traces of operators
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 61 (2006) no. 5, pp. 885-953

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This survey is devoted to the history and the current state of the theory of regularized traces of linear operators. The main focus is on operators with discrete spectrum. Several appendices are devoted to closely related areas of spectral theory and to the formulation of some important unsolved problems. 
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V. A. Sadovnichii; V. E. Podolskii. Traces of operators. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 61 (2006) no. 5, pp. 885-953. http://geodesic.mathdoc.fr/item/RM_2006_61_5_a1/