Lim-3 Durumundaki 4. Mertebe Operatörlerin Dissipatif Genişlemeleri

Yıl 2013, Cilt: 2 Sayı: 2, 75 - 79, 22.01.2014

Hüseyin Tuna

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

Öz

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

Anahtar Kelimeler

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

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

• 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.