Geodesic
On the computation of the spectrum of directionally perturbed operators
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 7, pp. 1179-1199 
E. M. Maleko. On the computation of the spectrum of directionally perturbed operators. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 7, pp. 1179-1199. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_7_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A class of operators with special spectral properties is defined. An operator in this class is fairly simple, acts in a separable Hilbert space, and can be perturbed so that an a priori given function from its domain is an eigenfunction of the perturbed operator. This fact is shown to be useful for constructing operators in mathematical physics. Specific examples are given.

[1] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii: funktsii Besselya, funktsii parabolicheskogo tsilindra, ortogonalnye mnogochleny, Nauka, M., 1974

[2] Maleko E. M., “O predstavlenii operatora s zaranee zadannoi sobstvennoi funktsiei”, Vestn. MaGU. Ser. matem., 9, MaGU, Magnitogorsk, 2006, 64–69 | Zbl

[3] Naimark M. A., Lineinye differentsialnye operatory, Gostekhteorizdat, M., 1954

[4] Maleko E. M., K vychisleniyu spektra diskretnykh i napravlenno vozmuschennykh operatorov, monografiya, MaGU, Magnitogorsk, 2007