Geodesic
Existence of eigenvalues of operators acting in $L^2(R^n)$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2017), pp. 30-40.

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

We write out conditions that help to prove the existence of eigenvalues and characteristic values for operator $F(D)-C(\lambda): L^{2}(R^{m})\to L^{2}(R^{m})$, where $F(D)$ is a pseudodifferential operator with a symbol $F(i\xi)$ and $C(\lambda): L^{2}(R^{m}) \to L^{2}(R^{m})$ is a linear continuous operator.
Keywords: pseudodifferential operator, characteristic values, eigenvalues. 
@article{IVM_2017_7_a3,
     author = {V. S. Mokeychev},
     title = {Existence of eigenvalues of operators acting in $L^2(R^n)$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {30--40},
     publisher = {mathdoc},
     number = {7},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_7_a3/}
}
TY  - JOUR
AU  - V. S. Mokeychev
TI  - Existence of eigenvalues of operators acting in $L^2(R^n)$
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2017
SP  - 30
EP  - 40
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2017_7_a3/
LA  - ru
ID  - IVM_2017_7_a3
ER  - 
%0 Journal Article
%A V. S. Mokeychev
%T Existence of eigenvalues of operators acting in $L^2(R^n)$
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2017
%P 30-40
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2017_7_a3/
%G ru
%F IVM_2017_7_a3
V. S. Mokeychev. Existence of eigenvalues of operators acting in $L^2(R^n)$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2017), pp. 30-40. http://geodesic.mathdoc.fr/item/IVM_2017_7_a3/

[1] Mokeichev V. S., “Problema sobstvennykh znachenii vo vsem prostranstve dlya uravnenii s razryvnymi koeffitsientami”, Izv. vuzov. Matem., 2002, no. 6, 45–49 | Zbl

[2] Mokeichev V. S., “Ob otsutstvii sobstvennykh znachenii u zadachi, obobschayushei zadachu o volnovodakh”, Izv. vuzov. Matem., 2004, no. 6, 41–47 | Zbl

[3] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969

[4] Mokeichev V. S., “Sobstvennye znacheniya psevdodifferentsialnykh operatorov”, Sovremen. metody teorii kraevykh zadach, Mater. Voronezhsk. vesennei matem. shkoly «Pontryaginskie chteniya–XXIV» (VGU, Voronezh, 2013), 129

[5] Shubin M. A., Psevdodifferentsialnye operatory i spektralnaya teoriya, Nauka, M., 1978

[6] Mokeichev V. S., “Suschestvovanie i bazisnost sobstvennykh i prisoedinennykh elementov lineinykh operatorov”, Izv. vuzov. Matem., 2008, no. 6, 43–55