Geodesic
Spectral properties of the generalized Friedrichs model
Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 1, pp. 17-33 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the self-adjoint generalized Friedrichs model with small values of the "coupling parameter". In this case, we completely investigate the spectrum of the model and the structure of its eigenvectors (both ordinary and generalized). The constructions we use are based on an analysis of the resolvent of the Friedrichs operator and on the corresponding scattering theory.
Keywords: generalized Friedrichs model, resolvent, spectrum, generalized eigenvector, wave operator. 
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E. R. Akchurin. Spectral properties of the generalized Friedrichs model. Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 1, pp. 17-33. http://geodesic.mathdoc.fr/item/TMF_2010_163_1_a1/

[1] K. O. Friedrichs, Math. Ann., 115:1 (1938), 249–272 | DOI | MR | Zbl

[2] S. N. Lakaev, “Some special properties of the generalized Friedrichs model”, Trudy seminara im. I. G. Petrovskogo, 11, 1986, 210–223 | MR | Zbl

[3] K. Fridrikhs, Vozmuschenie spektra operatorov v gilbertovom prostranstve, M., 1969 | MR | Zbl

[4] K. O. Friedrichs, Comm. Pure Appl. Math., 1:4 (1948), 361–406 | DOI | MR | Zbl

[5] L. D. Faddeev, Dokl. AN SSSR, 145:2 (1962), 301–304 | MR

[6] L. D. Faddeev, “O modeli Fridrikhsa v teorii vozmuschenii nepreryvnogo spektra”, Kraevye zadachi matematicheskoi fiziki. 2, Sbornik rabot. Posvyaschaetsya pamyati Vladimira Andreevicha Steklova v svyazi so stoletiem so dnya ego rozhdeniya, Trudy MIAN SSSR, 73, Nauka, M., 1964, 292–313 | MR | Zbl

[7] D. R. Yafaev, Matematicheskaya teoriya rasseyaniya, Izd-vo SPbGU, SPb., 1994 | MR | MR | Zbl

[8] S. P. Merkurev, L. D. Faddeev, Kvantovaya teoriya rasseyaniya dlya sistem neskolkikh chastits, Nauka, M., 1985 | MR | MR | Zbl

[9] N. Angelescu, R. A. Minlos, V. A. Zagrebnov, Rev. Math. Phys., 17:10 (2005), 1111–1142 | DOI | MR | Zbl

[10] K. Boldrigini, R. A. Minlos, A. Pellegrinotti, UMN, 62:4(376) (2007), 27–76 | DOI | MR | Zbl

[11] E. L. Lakshtanov, R. A. Minlos, Funkts. analiz i ego pril., 38:3 (2004), 52–69 | DOI | MR | Zbl

[12] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii i deistviya nad nimi, Vyp. 1, Fizmatlit, M., 1959 | MR | Zbl

[13] I. I. Privalov, Granichnye svoistva analiticheskikh funktsii, Gostekhizdat, M.-L., 1950 | MR | Zbl

[14] N. I. Muskhelishvili, Singulyarnye integralnye uravneniya, Nauka, M., 1968 | MR | MR | Zbl

[15] S. Bochner, Fundam. Math., 20 (1933), 262–276 | Zbl

[16] K. Iosida, Funktsionalnyi analiz, Mir, M., 1967 | MR | MR | Zbl

[17] N. I. Akhiezer, I. M. Glazman, Teoriya lineinykh operatorov v gilbertovom prostranstve, Nauka, M., 1966 ; | MR | MR | Zbl | MR | MR

[18] C. Boldrighini, R. A. Minlos, A. Pellegrinotti, Probab. Theory Relat. Fields, 129:1 (2004), 133–156 | DOI | MR | Zbl

[19] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki. T. 4. Analiz operatorov, Mir, M., 1982 | MR | MR | Zbl

[20] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki. T. 3. Teoriya rasseyaniya, Mir, M., 1982 | MR | MR | Zbl

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

[22] V. I. Paraska, Matem. sb., 68(110):4 (1965), 623–631 | MR | Zbl