Lim-3 Durumundaki 4. Mertebe Operatörlerin Dissipatif Genişlemeleri

Year 2013, Volume: 2 Issue: 2, 75 - 79, 22.01.2014

Hüseyin Tuna

https://doi.org/10.17100/nevbiltek.210890

Abstract

Bu çalışmada, Lim-3 durumundaki skaler 4.
mertebeden difereasiyel operatörlerinin maksimal dissipatif, kendine eş ve
diğer genişlemeleri verilmiştir.

Keywords

Dissipatif genişlemeler, kendine eş genişlemeler, sınır değer uzayı, sınır koşulu

Dissipative Extensions of Fourth Order Differential Operators in the Lim -3 Case

Abstract

In this article, we give a description of
all maximal dissipative, self adjoint and other extensions of scalar fourth
order differential operators in the lim 3 case.

Keywords

Dissipative extensions, self adjoint extensions, a boundary value space, boundary condition

References

• Von Neumann J., “Allgemeine Eigenwertheorie Hermitischer Functionaloperatoren”, Math. Ann. 102,49-131, 1929.
• Calkin J. W., “Abstract boundary conditions”, Trans. Amer. Math. Soc.,45, 3, 369-442, 1939. Rofe-Beketov F.S., “Self-adjoint extensions of differential operators in a space of vector valued functions'”, Dokl. Akad. Nauk SSSR 184,1034-1037, 1969 ; English transl. in Soviet Math. Dokl. 10,188-192, 1969.
• Bruk V. M. “On a class of boundary --value problemswith a spectral parameter in the boundary conditions”, Mat. Sb., 100, 210-216. , 1976.
• Kochubei A. N., “Extensions of symmetric operators and symmetric binary relations”, Mat. Zametki 17, 41-48, 1975; English transl. in Math. Notes 17, 25-28, 1975.
• Gorbachuk M.L., “Gorbachuk V.I. and Kochubei A.N., The theory of extensions of symmetric operators and boundary-value problems for differential equations”, Ukrain. Mat. Zh. 4112991312, 1989; English transl. in Ukrainian Math. J. 41, 1117-1129, 1989.
• Fulton C.T., “Parametrization of Titchmarsh"s m (λ)- functions in the limit circle case”, Trans. Amer. Math. Soc. 229, 51-63 , 1977.
• Krein M. G., “On the indeterminate case of the Sturm-Liouville boundaryvalue problem in the interval (0,∞)”, Akad. Nauk SSSR Ser. Mat. 16, 292-324, 1952.
• Khol'kin A. M., “Self-adjoint boundary conditions at-infinity for a quasi regular system of evenorder differential equations”, 174-183 in: Theory of operators in function spaces and its applications, Naukova Dumka, Kiev, 1981.
• Mirzoev G. A., “Fourth order quasi regular differential operator” Dokl. Akad. Nauk SSSR 251, no.3, 550-553, 1980; English transl. Soviet Math. Dpkl. 21, 480-483, 1980.
• Gorbachuk M. L., “On spectral functions of a second order differential operator with operator coefficients”, Ukrain. Mat. Zh. 18, no.2, 3-21, 1966; English transl. Amer. Math. Soc. Transl. Ser. II 72, 177-202, 1968.
• Allahverdiev B. P., “On extensions of symmetric Schrödinger operators with a matrix potential”, Izvest. Ross. Akad. Nauk. Ser . Math. 59, 19-54, 1995; English transl. Izv. Math. 59, 45-62, 19
• Guseĭnov I. M. and Pashaev R. T., “Description of self adjoint extensions of a class of differential operators of order 2n with defect indices (n+k,,n+k),0<k<n”, Izv.Akad.Nauk Azerb. Ser. Fiz. Tekh. Mat. Nauk, No.2, 15-19 (in Russian) , 1983.
• Maksudov F.G. and Allahverdiev B.P., “On the extensions of Schrödinger operators with a matrix potentials”, Dokl. Akad. Nauk 332, no.118-20, 1993,;English transl. Russian Acad. Sci. Dokl. Math. 48 no.2, 240-243, 1994.
• Malamud M. M. and Mogilevskiy V. I., “On extensions of dual pairs of operators, Dopov”. Nats Akad. Nauk. Ukr. no. 1, 30-37, 1997.
• Mogilevskiy V. I., “On proper extensions of a singular differential operator in a space of vector functions”, Dopov. Akad. Nauk. Ukraini, no.9, 29-33 (in Russian) , 1994.
• Naimark M. A., “Linear Differential Operators”, 2nd edn.,1968, Nauka, Moscow, English transl. of 1st. edn., 1,2, New York, 1969.
• Gorbachuk M. L. and Gorbachuk V. I., “Boundary Value Problems for Operator Differential Equations”, Naukova Dumka, Kiev, 1984; English transl., Birkhauser Verlag 1991.