Geodesic
An abstract formula for regularized traces of discrete operators and its applications
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 4, Tome 193 (2021), pp. 142-152

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In this paper, we prove an abstract formula for regularized traces of discrete operators in a separable Hilbert space. This formula is a generalization of the formula for the first regularized trace to the case of higher-order traces. We also discuss applications of the formula obtained to a wide class of discrete operators acting in the Bergman space that are generalizations of the Gribov operator from Reggeon field theory.
Keywords: Hilbert space, discrete operator, linear non-self-adjoint operator, spectral theory, regularized trace formula, Bergman space, Reggeon field theory, Gribov operator. 
@article{INTO_2021_193_a14,
     author = {N. G. Tomin and I. V. Tomina},
     title = {An abstract formula for regularized traces of discrete operators and its applications},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {142--152},
     publisher = {mathdoc},
     volume = {193},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_193_a14/}
}
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N. G. Tomin; I. V. Tomina. An abstract formula for regularized traces of discrete operators and its applications. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 4, Tome 193 (2021), pp. 142-152. http://geodesic.mathdoc.fr/item/INTO_2021_193_a14/