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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - N. G. Tomin
AU  - I. V. Tomina
TI  - An abstract formula for regularized traces of discrete operators and its applications
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2021
SP  - 142
EP  - 152
VL  - 193
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2021_193_a14/
LA  - ru
ID  - INTO_2021_193_a14
ER  - 
%0 Journal Article
%A N. G. Tomin
%A I. V. Tomina
%T An abstract formula for regularized traces of discrete operators and its applications
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2021
%P 142-152
%V 193
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2021_193_a14/
%G ru
%F INTO_2021_193_a14
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/

[1] Boreskov K. G., Kaidalov A. B., Kancheli O. V., “Silnye vzaimodeistviya pri vysokoi energii v redzheonnom podkhode”, Yad. fiz., 69:10 (2006), 1802–1818

[2] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gilbertovom prostranstve, Nauka, M., 1965

[3] Gribov V. N., “Tekhnika diagramm Redzhe”, ZhETF., 53 (1967), 654–672

[4] Sadovnichii V. A., Konyagin S. V., Podolskii V. E., “Regulyarizovannyi sled operatora s yadernoi rezolventoi, vozmuschennogo ogranisennym”, Dokl. RAN., 373:1 (2000), 26–28 | MR | Zbl

[5] Sadovnichii V. A., Podolskii V. E., “Regulyarizovannyi sled ogranichennogo vozmuscheniya operatora s yadernoi rezolventoi”, Differ. uravn., 34:4 (1999), 556–564

[6] Sadovnichii V. A., Podolskii V. E., “Sledy operatorov s otnositelno yadernym vozmuscheniem”, Dokl. RAN., 378:3 (2001), 1–2

[7] Sadovnichii V. A., Podolskii V. E., “Sledy operatorov s otnositelno kompaktnym vozmuscheniem”, Mat. sb., 193:2 (2002), 129–152 | MR | Zbl

[8] Tomin N. G., “O pervom regulyarizovannom slede diskretnogo operatora”, Tez. dokl. Mezhdunar. konf., posv. 90-letiyu so dnya rozhd. L. S. Pontryagina, MGU, M., 1998, 165–167

[9] Tomin N. G., “O nekotorykh formulakh pervogo regulyarizovannogo sleda dlya diskretnykh operatorov”, Mat. zametki., 70:1 (2001), 109–122 | MR | Zbl

[10] Tomin N. G., Tomina I. V., “Ob odnoi abstraktnoi formule regulyarizovannykh sledov diskretnykh operatorov i ee primeneniyakh”, Mat. Mezhdunar. konf. «Voronezhskaya vesennyaya matematicheskaya shkola «Pontryaginskie chteniya–XXX», Izdatelskii dom VGU, Voronezh, 2019, 273–274

[11] Bargmann V., “On a Hilbert space of analytic functions and an associated integral transform, I”, Commun. Pure Appl. Math., 14 (1961), 187–214 | DOI | MR | Zbl

[12] Intissar A., “Regularized trace formula of magic Gribov operator on Bargmann space”, J. Math. Anal. Appl., 437:1 (2016), 59–70 | DOI | MR | Zbl

[13] Tomin N. G., “One regularized trace formula of discrete operators”, Mat. Mezhdunar. nauch. konf. «Teoriya priblizheniya funktsii i rodstvennye zalachi analiza», posv. pamyati d.f.-m.n., professora P. K. Korovkina, Izd-vo KGU im. K. E. Tsiolkovskogo, Kaluga, 2015