Geodesic
Correct and selfadjoint problems for quadratic operators
Eurasian mathematical journal, Tome 1 (2010) no. 2, pp. 122-135.

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

In this paper we present a simpler method of proving the correctness and selfadjointtness of the operators of the form $B^2$ corresponding to some boundary value problems. We also give explict representations for the unique solution of these problems. 
@article{EMJ_2010_1_2_a8,
     author = {I. N. Parasidis and P. C. Tsekrekos},
     title = {Correct and selfadjoint problems for quadratic operators},
     journal = {Eurasian mathematical journal},
     pages = {122--135},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2010_1_2_a8/}
}
TY  - JOUR
AU  - I. N. Parasidis
AU  - P. C. Tsekrekos
TI  - Correct and selfadjoint problems for quadratic operators
JO  - Eurasian mathematical journal
PY  - 2010
SP  - 122
EP  - 135
VL  - 1
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2010_1_2_a8/
LA  - en
ID  - EMJ_2010_1_2_a8
ER  - 
%0 Journal Article
%A I. N. Parasidis
%A P. C. Tsekrekos
%T Correct and selfadjoint problems for quadratic operators
%J Eurasian mathematical journal
%D 2010
%P 122-135
%V 1
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2010_1_2_a8/
%G en
%F EMJ_2010_1_2_a8
I. N. Parasidis; P. C. Tsekrekos. Correct and selfadjoint problems for quadratic operators. Eurasian mathematical journal, Tome 1 (2010) no. 2, pp. 122-135. http://geodesic.mathdoc.fr/item/EMJ_2010_1_2_a8/

[1] E. A. Coddington, “Self-adjoint subspace extensions of nondensely defined symmetric operators”, Adv. Math., 14 (1974), 309–332 | DOI | MR | Zbl

[2] E. A. Coddington, A. Dijksma, “Self-adjoint subspaces and eigenfunction expansions for ordinary differential subspaces”, J. Diff. Equat., 20 (1976), 473–526 | DOI | MR | Zbl

[3] A. A. Dezin, General aspects of Boundary Value problems, Nauka, Moskva, 1980 (in Russian) | MR | Zbl

[4] V. I. Gorbachuk, M. L. Gorbachuk, Boundary Value Problems for Operator Differential equations, Kluwer, Dordrecht, 1991 | MR | Zbl

[5] T. Sh. Kalmenov, “On regular extensions for the semiminimal Lavrentiev–Bitsadze operator”, Diff. Eq., 18:1 (1982), 193–199 (in Russian) | MR

[6] A. N. Kochubei, “Extensions of positive definite symmetric operators”, Doklady Acad. Nauk Ukraine. Ser. A, 3 (1979), 168–171 (in Russian) | MR

[7] A. N. Kochubei, “Extensions of a nondensely defined symmetric operator”, Sib. Math. J., 18 (1977), 225–229 (in Russian) | DOI | MR

[8] B. K. Kokebaev, M. Otelbaev, A. N. Shynibekov, “About Restrictions and Extensions of operators”, Doklady Acad. Nauk USSR, 271:6 (1983), 1307–1310 (in Russian) | MR | Zbl

[9] B. A. Mikhailets, “The spectrum of operators and boundary value problems, spectral analysis of differential operators”, Proc. Inst. of Math. Ukrain Academy, 1980, 106–131 (in Russian) | MR

[10] J. von Neumann, “Allgemeine Eigenwerttheorie Hermitescher Functional operatoren”, Math. Ann., 102 (1929–1930), 49–131 | MR | Zbl

[11] R. O. Oinarov, I. N. Parasidi, “Correct extensions of operators with finite defect in Banach spases”, Izv. Akad. Kaz. SSR, 5 (1988), 42–46 (in Russian) | MR

[12] R. O. Oinarov, S. S. Sagintaeva, “Smooth expansions of minimal operator in Banach spase”, Izv. Acad. Nauk Resp. Kaz., 5 (1994), 43–48 (in Russian) | MR

[13] I. N. Parasidis, P. C. Tsekrekos, “Correct selfadjoint and positive extensions of nondensely defined symmetric operators”, Abstract and Applied Analysis, 7, Hindawi Publishing Corporation, 2005, 767–790 | DOI | MR

[14] A. N. Shynibekov, On correct extensions and restrictions for some differential operators, Candidate's degree thesis, Inst. Math. AS KazSSR, Alma-Ata, 1983 (in Russian)

[15] M. I. Vishik, “About Boundary Value Problems for Elliptical Differential equations”, Mosk. Math. Society, 1, 1952, 187–246 (in Russian)