Almost periodicity in spectral analysis representations induced by generalized shift operation
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2012), pp. 9-13.

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

The famous Theorem of Yu. Lubich allows us in the language of the almost periodicity to get the criterion of completeness of the eigenvectors of a Hermitian compact operator in a weakly complete Banach space. In this paper this result is strengthened for the representation generated by the operation of the generalized shift.
Keywords: representations, generalized shift operations, almost periodicity.
@article{UZERU_2012_3_a1,
     author = {M. I. Karakhanian},
     title = {Almost periodicity in spectral analysis representations induced by generalized shift operation},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {9--13},
     publisher = {mathdoc},
     number = {3},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2012_3_a1/}
}
TY  - JOUR
AU  - M. I. Karakhanian
TI  - Almost periodicity in spectral analysis representations induced by generalized shift operation
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2012
SP  - 9
EP  - 13
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_2012_3_a1/
LA  - en
ID  - UZERU_2012_3_a1
ER  - 
%0 Journal Article
%A M. I. Karakhanian
%T Almost periodicity in spectral analysis representations induced by generalized shift operation
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2012
%P 9-13
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_2012_3_a1/
%G en
%F UZERU_2012_3_a1
M. I. Karakhanian. Almost periodicity in spectral analysis representations induced by generalized shift operation. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2012), pp. 9-13. http://geodesic.mathdoc.fr/item/UZERU_2012_3_a1/

[1] K. Yosida, Functional Analysis, Springer Verlag, Berlin–Gottingen–Heidelberg, 1985

[2] Yu.I. Ljubich, “Almost periodical functions in the spectral analysis of operators”, Doklady Akad. Nauk SSSR, 132:3 (1960), 518–520 (in Russian) | MR

[3] Yu. I. Lyubich, “Completeness conditions for a system of eigenvectors of a correct operator”, Uspekhi Mat. Nauk, 18:1(109) (1963), 165–171 (in Russian) | MR | Zbl

[4] M.I. Karakhanyan, “Almost-periodicity in the spectral analysis of normal operators”, Izvestia Akad. Nauk Arm. SSR, 83:4 (1986), 154–157 (in Russian) | MR | Zbl

[5] M.I. Karakhanyan, “On the Fullness Conditions of the Eigenvector System of General Normal Operators”, Uchenie Zapiski EGU, 1988, no. 3 (169), 3–8 (in Russian) | MR | Zbl

[6] Yu.I. Ljubich, Introduction to the Banach Representations of Groups, Visha Shkola, Kharkov, 1985 (in Russian)

[7] B.M. Levitan, Generalised Shift Operations and Some Applications, Nauka, M., 1962 (in Russian)

[8] M.A. Naimark, Normed Rings, Nauka, M., 1964 (in Russian) | MR

[9] H. Weyl, “Integralgleichungen und Fastperiodische Funktionen”, Math. Ann., 37 (1927), 338–356. | DOI | MR

[10] B. Lewitan, “Die Verallgemeinerung der Operation der Verschiebung im Zusammenhang mit fastperiodischen Funktionen”, Rec. Math. [Mat. Sbornik] N.S., 7(49):3 (1940), 449–478 | MR | Zbl

[11] A. I. Shtern, “Representation of Topological Groups in Locally Convex Space: Continuity Properties and Weak Almost Periodicity”, Russian J. Math. Phys., 11:1 (2004), 81–108 | MR

[12] Russian Math. Surveys, 60:3 (2005), 489–557 | DOI | DOI | MR | Zbl

[13] S. Banach, Theorie des Operations Linearies, Warsaw, 1932

[14] N. Dunford, J.T. Shwartz, Linear Operators, v. I, General Theory, New York–London, 1958