Geodesic
Matrix Eigenvalues in Analytic Perturbation Theory for Linear Operators
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 3, pp. 158-172 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the present paper, we propose a new approach to the analytic perturbation theory for isolated eigenvalues of finite multiplicity. This approach is based on the notion of the matrix eigenvalue of a linear operator. As an application example, we consider linear problems for differential equations.
Keywords: linear operator, analytic perturbation theory.
Mots-clés : matrix eigenvalue 
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V. S. Mokeichev; A. M. Sidorov. Matrix Eigenvalues in Analytic Perturbation Theory for Linear Operators. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 3, pp. 158-172. http://geodesic.mathdoc.fr/item/UZKU_2012_154_3_a14/

[1] Schrödinger E., “Quantisierung als Eigenwertproblem. Dritte Mitteilung: Störungstheorie, mit Anwendung auf den Starkeffekt der Balmerlinien”, Ann. Phys., 80 (1926), 437–490 | DOI | Zbl

[2] Rellich F., “Störungstheorie der Spektralzerlegung. I: Mitteilung. Analytische Störung der isolierten Punkteigenwerte eines beschränkten Operators”, Math. Ann., 113 (1937), 600–619 | DOI | MR

[3] Mokeichev V. S., “Sobstvennye znacheniya granichnykh zadach. Preobrazovanie granichnykh zadach k granichnym zadacham s malymi koeffitsientami”, Differents. uravneniya, 25:2 (1989), 222–228 | MR

[4] Mokeichev V. S., Sidorov A. M., “O matrichnom podkhode k teorii vozmuschenii lineinykh operatorov”, Sovremennye metody teorii funktsii i smezhnye problemy, Materialy konf. Voronezh. zimnei matem. shkoly, Izd.-poligraf. tsentr Voronezh. un-ta, Voronezh, 2009, 119–120

[5] Sidorov A. M., “Matrichnye sobstvennye znacheniya v teorii vozmuschenii”, Sovremennye problemy teorii funktsii i ikh prilozhenii, Materialy 16-i Sarat. zimnei shkoly, Nauchn. shk., Saratov, 2012, 161–162

[6] Bari N. K., “Biortogonalnye sistemy i bazisy v gilbertovom prostranstve”, Uchen. zap. Mosk. gos. un-ta, 4:148 (1951), 69–107 | MR

[7] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969, 528 pp.