BibTex RIS Kaynak Göster

Lim-3 Durumundaki 4. Mertebe Operatörlerin Dissipatif Genişlemeleri

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

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.

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

Yıl 2013, Cilt: 2 Sayı: 2, 75 - 79, 22.01.2014
https://doi.org/10.17100/nevbiltek.210890

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.

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.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Matematik
Yazarlar

Hüseyin Tuna

Yayımlanma Tarihi 22 Ocak 2014
Yayımlandığı Sayı Yıl 2013 Cilt: 2 Sayı: 2

Kaynak Göster

APA Tuna, H. (2014). Dissipative Extensions of Fourth Order Differential Operators in the Lim -3 Case. Nevşehir Bilim Ve Teknoloji Dergisi, 2(2), 75-79. https://doi.org/10.17100/nevbiltek.210890
AMA Tuna H. Dissipative Extensions of Fourth Order Differential Operators in the Lim -3 Case. Nevşehir Bilim ve Teknoloji Dergisi. Ocak 2014;2(2):75-79. doi:10.17100/nevbiltek.210890
Chicago Tuna, Hüseyin. “Dissipative Extensions of Fourth Order Differential Operators in the Lim -3 Case”. Nevşehir Bilim Ve Teknoloji Dergisi 2, sy. 2 (Ocak 2014): 75-79. https://doi.org/10.17100/nevbiltek.210890.
EndNote Tuna H (01 Ocak 2014) Dissipative Extensions of Fourth Order Differential Operators in the Lim -3 Case. Nevşehir Bilim ve Teknoloji Dergisi 2 2 75–79.
IEEE H. Tuna, “Dissipative Extensions of Fourth Order Differential Operators in the Lim -3 Case”, Nevşehir Bilim ve Teknoloji Dergisi, c. 2, sy. 2, ss. 75–79, 2014, doi: 10.17100/nevbiltek.210890.
ISNAD Tuna, Hüseyin. “Dissipative Extensions of Fourth Order Differential Operators in the Lim -3 Case”. Nevşehir Bilim ve Teknoloji Dergisi 2/2 (Ocak 2014), 75-79. https://doi.org/10.17100/nevbiltek.210890.
JAMA Tuna H. Dissipative Extensions of Fourth Order Differential Operators in the Lim -3 Case. Nevşehir Bilim ve Teknoloji Dergisi. 2014;2:75–79.
MLA Tuna, Hüseyin. “Dissipative Extensions of Fourth Order Differential Operators in the Lim -3 Case”. Nevşehir Bilim Ve Teknoloji Dergisi, c. 2, sy. 2, 2014, ss. 75-79, doi:10.17100/nevbiltek.210890.
Vancouver Tuna H. Dissipative Extensions of Fourth Order Differential Operators in the Lim -3 Case. Nevşehir Bilim ve Teknoloji Dergisi. 2014;2(2):75-9.

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