Regularized Trace of the Dirac Operator
Matematičeskie zametki, Tome 98 (2015) no. 1, pp. 134-146.

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

Formulas for the regularized trace of the one-dimensional non–self-adjoint Dirac operator with $L^2$-potential are obtained. The cases of periodic and antiperiodic boundary conditions as well as of the Dirichlet boundary conditions are considered. The formulas are obtained by using the method of similar operators on the basis of results from the papers [1] and [2].
Keywords: non–self-adjoint Dirac operator, regularized trace, periodic/antiperiodic boundary conditions, Dirichlet boundary conditions, Hilbert space, complex Banach space, Banach algebra
Mots-clés : Fourier coefficient.
@article{MZM_2015_98_1_a9,
     author = {A. O. Shcherbakov},
     title = {Regularized {Trace} of the {Dirac} {Operator}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {134--146},
     publisher = {mathdoc},
     volume = {98},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_1_a9/}
}
TY  - JOUR
AU  - A. O. Shcherbakov
TI  - Regularized Trace of the Dirac Operator
JO  - Matematičeskie zametki
PY  - 2015
SP  - 134
EP  - 146
VL  - 98
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2015_98_1_a9/
LA  - ru
ID  - MZM_2015_98_1_a9
ER  - 
%0 Journal Article
%A A. O. Shcherbakov
%T Regularized Trace of the Dirac Operator
%J Matematičeskie zametki
%D 2015
%P 134-146
%V 98
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2015_98_1_a9/
%G ru
%F MZM_2015_98_1_a9
A. O. Shcherbakov. Regularized Trace of the Dirac Operator. Matematičeskie zametki, Tome 98 (2015) no. 1, pp. 134-146. http://geodesic.mathdoc.fr/item/MZM_2015_98_1_a9/

[1] A. G. Baskakov, “Metod podobnykh operatorov i formuly regulyarizovannykh sledov”, Izv. vuzov. Matem., 1984, no. 3, 3–12 | MR | Zbl

[2] A. G. Baskakov, A. V. Derbushev, A. O. Scherbakov, “Metod podobnykh operatorov v spektralnom analize nesamosopryazhennogo operatora Diraka s negladkim potentsialom”, Izv. RAN. Ser. matem., 75:3 (2011), 3–28 | DOI | MR | Zbl

[3] B. S. Mityagin, P. Dzhakov, “Zony neustoichivosti odnomernykh periodicheskikh operatorov Shredingera i Diraka”, UMN, 61:4 (2006), 77–182 | DOI | MR | Zbl

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

[5] V. A. Sadovnichii, V. E. Podolskii, “Sledy operatorov”, UMN, 61:5 (2006), 89–156 | DOI | MR | Zbl

[6] A. M. Savchuk, I. V. Sadovnichaya, “Asimptoticheskie formuly dlya fundamentalnykh reshenii sistemy Diraka s kompleksnoznachnym summiruemym potentsialom”, Differents. uravneniya, 49:5 (2013), 573–584 | MR | Zbl

[7] A. G. Baskakov, Garmonicheskii analiz lineinykh operatorov, Izd-vo Voronezhsk. gos. un-ta, Voronezh, 1987 | MR

[8] A. G. Baskakov, “Spektralnyi analiz vozmuschennykh nekvazianaliticheskikh i spektralnykh operatorov”, Izv. RAN. Ser. matem., 58:4 (1994), 3–32 | MR | Zbl

[9] A. G. Baskakov, “Formuly regulyarizovannykh sledov dlya stepenei vozmuschennykh spektralnykh operatorov”, Izv. vuzov. Matem., 1985, no. 8, 68–71 | MR | Zbl

[10] A. Zigmund, Trigonometricheskie ryady, T. 1, 2, Mir, M., 1965 | MR | Zbl | Zbl