Schrödinger-type operator over $p$-adic number field
Teoretičeskaâ i matematičeskaâ fizika, Tome 86 (1991) no. 3, pp. 323-333 Cet article a éte moissonné depuis la source Math-Net.Ru

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The spectral properties of a Schrödinger-type $p$-adic operator are studied. The self-adjointness of the minimal operator is proved. The completeness of the eigenvectors, the asymptotic behavior of the eigenvalues, and the position of the essential spectrum are considered.
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     author = {A. N. Kochubei},
     title = {Schr\"odinger-type operator over $p$-adic number field},
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A. N. Kochubei. Schrödinger-type operator over $p$-adic number field. Teoretičeskaâ i matematičeskaâ fizika, Tome 86 (1991) no. 3, pp. 323-333. http://geodesic.mathdoc.fr/item/TMF_1991_86_3_a0/

[1] Vladimirov V. S., UMN, 43:5 (1988), 17–53 | MR | Zbl

[2] Vladimirov V. S., Volovich I. V., Zelenov E. I., Izv. AN SSSR. Ser. matem., 54:2 (1990), 275–302 | MR | Zbl

[3] Vladimirov V. S., Volovich I. V., Lett. Math. Phys., 18:1 (1989), 43–53 | DOI | MR | Zbl

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

[5] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl

[6] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, t. 1, Mir, M., 1977 | MR

[7] Lankaster P., Teoriya matrits, Nauka, M., 1978 | MR

[8] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, t. 4, Mir, M., 1982 | MR

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

[10] Khua L., Metod trigonometricheskikh summ i ego primeneniya v teorii chisel, Mir, M., 1964 | MR

[11] Weyl H., Math. Ann., 77 (1916), 313–352 | DOI | MR | Zbl

[12] Korobov N. M., Izv. AN SSSR. Ser. matem., 19:5 (1955), 361–380 | MR | Zbl

[13] Postnikov A. G., UMN, 16:3 (1961), 201–205 | MR | Zbl

[14] Kulikova M. F., DAN SSSR, 143:4 (1962), 782–784 | MR | Zbl