On Basis Property for a Boundary-Value Problem with a Spectral Parameter in the Boundary Condition
Yıl 2006,
Cilt: 1 Sayı: 5, 9 - 17, 01.04.2006
Vagif Y. Gul, Khanlar R. Mamedov
Khanlar R. Mamedov
Kaynakça
- T. J. Azizov, İ. C. İokhidov, OsnoniTteorii Lineynikh Operatoroc v Prostranstrax s Indedinitnoy Metrikoy (Linear Operators in Spaces With an Indefinite Metric) (Moscow: Nauka, 1986) (Russian)
- P. A. Binding, P.J. Browne, K. Siddighi, ‘Sturm-Louville Problems with Eigenparameter Dependent Conditions’, Proc. Edinburgh Math. Soc. V.37, No.1 (1999), pp.57-72
- P. A. Binding, P.J. Browne,B.A.Watson, ‘Sturm-Louville Problems with Boundary Conditions rationally dependent on the eigenparameter I’, Proc. Edinburg Math. Soc.45 (2002) pp, 631- 645.
- P. A. Binding, P.J. Browne,B.A.Watson, ‘Sturm-Louville Problems with Boundary Conditions rationally dependent on the eigenparameter II’, Journal of Comp. and Appl. Math. 148 (2002), pp.147-168.
- N. J. Guliyev, ‘Inverse Eigenvalue Problems for Sturm-Liouville Equations with Spectral Parameter Linearly Contained in one the Boundary Conditions’, Inverse Problems, 21 (2005) pp.1315-1330
- C. T. Fulton, ‘Two-point Boundary Value Problems with Eigen-value Parameter Contained in the Boundary Conditions’ Proc. Roy. Soc. Edin., 77 A (1977), pp.293-308.
- D. B. Hinton, ‘An Expansion Theorem for an Eigenvalue Problem with Eigenvalue Parameter in the Boundary Condition’, Quart. J. Math. Oxford, 30, No.2 (1979), pp.33-42
- N. Yu. Kapustin, E. İ. Moisseev, ‘Spectral Problem with the Spectral Parameter in the Boundary Condition’, Diff. Equations . V. 33 No.1 (1997), pp.115-119
- N. Yu. Kapustin, E. İ. Moisseev, ‘On the Spectral Problem from the Theory of the Parabolic Heat Equation’, Dok. Russ. Akad. Nauk, 352 No.4 (1997), pp.451-454
- N. Yu. Kapustin, E. İ. Moisseev ‘Oscillation Properties of the Solutions to a Nonselfadjoint Spectral Parameter in the Boundary Condition’, Diff. Equations ., V. 35 No.8 (1999), pp.1024- 1027
- N. Yu. Kapustin, , E. İ. Moisseev, ‘A remark On the Convergence problem for Spectral expansions Corresponding to Classical problem with a spectral Parameter in the Boundary Condition’, Diff. Equations, 37 V.(12) (2001), pp.1677-1683
- N. B. Kerimov, V. S. Mirzoev, ‘On the Basis Properties of the One Spectral Problem with a Spectral Parameter in a Boundaray Condition’, Siberian Mathematical Journal, V.44, No.5 (2003), pp.813-816
- N. B. Kerimov, Kh. R. Mamedov, ‘On a Boundary Value Problem with a Spectral Parameter in Boundary Conditions’, Siberian Mathematical Journal, V.40, No.2 (1999), pp.281-290
- Kh. R. Mamedov, ‘On one Boundary Value Problem with Parameter in the Boundary Conditions’, Spektralmaya teoriya operatorov i prilojeniya, N.11 (1997), pp. 117-121
- N. B. Kerimov, Kh. R. Mamedov, “The Sturm-Liouville Problem with Non-linear Spectral Parameter in the Boundary Conditions”, İzv.NAS Az., V.21, No 1 (2001), pp.100-104
- Kh. R. Mamedov, ‘Uniqueness of Solution of the Scattering Theory with a Spectral Parameter in the Boundary Condition’, Math. Notes. 74, (1) (2003), pp.136-140
- E. M. Russakovskij, ‘Operator treatment of boundary problems with spectral parameters entering via polynomials in the boundary conditions’, Funct. Anal. Appl. 9, (1975); pp.358-359 (translation from Funkts. Anal. i Prilozh. 9, No.4, (1975), pp.91-92) (Russian, English)
- A. A. Shkalikov, ‘Boundary Value Problems for Ordinary Differential Equations with a Spectral Parameter in the Boundary Conditions’, Trudy Sem. İm. İ. G. Petrovsogo, V.9 (1983), pp.190- 229
- A. N. Tikhonov, A. A. Samarskii, Equations of Mathematical Physics (Dover Books on Physics and Chemistry, 1990)
- J. Walter, ‘Regular Eigenvalue Problems with Eigenvalue Parameter in the Boundary Conditions’, Math. Z., 133 (1973), pp. 301-312.
On Basis Property for a Boundary-Value Problem with a Spectral Parameter in the Boundary Condition
Yıl 2006,
Cilt: 1 Sayı: 5, 9 - 17, 01.04.2006
Vagif Y. Gul, Khanlar R. Mamedov
Khanlar R. Mamedov
Öz
In the present work, the properties as completeness, minimality and basis property are investigated
for the eigenfunctions of Sturm-Liouville problem with a spectral parameter in the boundary condition
Kaynakça
- T. J. Azizov, İ. C. İokhidov, OsnoniTteorii Lineynikh Operatoroc v Prostranstrax s Indedinitnoy Metrikoy (Linear Operators in Spaces With an Indefinite Metric) (Moscow: Nauka, 1986) (Russian)
- P. A. Binding, P.J. Browne, K. Siddighi, ‘Sturm-Louville Problems with Eigenparameter Dependent Conditions’, Proc. Edinburgh Math. Soc. V.37, No.1 (1999), pp.57-72
- P. A. Binding, P.J. Browne,B.A.Watson, ‘Sturm-Louville Problems with Boundary Conditions rationally dependent on the eigenparameter I’, Proc. Edinburg Math. Soc.45 (2002) pp, 631- 645.
- P. A. Binding, P.J. Browne,B.A.Watson, ‘Sturm-Louville Problems with Boundary Conditions rationally dependent on the eigenparameter II’, Journal of Comp. and Appl. Math. 148 (2002), pp.147-168.
- N. J. Guliyev, ‘Inverse Eigenvalue Problems for Sturm-Liouville Equations with Spectral Parameter Linearly Contained in one the Boundary Conditions’, Inverse Problems, 21 (2005) pp.1315-1330
- C. T. Fulton, ‘Two-point Boundary Value Problems with Eigen-value Parameter Contained in the Boundary Conditions’ Proc. Roy. Soc. Edin., 77 A (1977), pp.293-308.
- D. B. Hinton, ‘An Expansion Theorem for an Eigenvalue Problem with Eigenvalue Parameter in the Boundary Condition’, Quart. J. Math. Oxford, 30, No.2 (1979), pp.33-42
- N. Yu. Kapustin, E. İ. Moisseev, ‘Spectral Problem with the Spectral Parameter in the Boundary Condition’, Diff. Equations . V. 33 No.1 (1997), pp.115-119
- N. Yu. Kapustin, E. İ. Moisseev, ‘On the Spectral Problem from the Theory of the Parabolic Heat Equation’, Dok. Russ. Akad. Nauk, 352 No.4 (1997), pp.451-454
- N. Yu. Kapustin, E. İ. Moisseev ‘Oscillation Properties of the Solutions to a Nonselfadjoint Spectral Parameter in the Boundary Condition’, Diff. Equations ., V. 35 No.8 (1999), pp.1024- 1027
- N. Yu. Kapustin, , E. İ. Moisseev, ‘A remark On the Convergence problem for Spectral expansions Corresponding to Classical problem with a spectral Parameter in the Boundary Condition’, Diff. Equations, 37 V.(12) (2001), pp.1677-1683
- N. B. Kerimov, V. S. Mirzoev, ‘On the Basis Properties of the One Spectral Problem with a Spectral Parameter in a Boundaray Condition’, Siberian Mathematical Journal, V.44, No.5 (2003), pp.813-816
- N. B. Kerimov, Kh. R. Mamedov, ‘On a Boundary Value Problem with a Spectral Parameter in Boundary Conditions’, Siberian Mathematical Journal, V.40, No.2 (1999), pp.281-290
- Kh. R. Mamedov, ‘On one Boundary Value Problem with Parameter in the Boundary Conditions’, Spektralmaya teoriya operatorov i prilojeniya, N.11 (1997), pp. 117-121
- N. B. Kerimov, Kh. R. Mamedov, “The Sturm-Liouville Problem with Non-linear Spectral Parameter in the Boundary Conditions”, İzv.NAS Az., V.21, No 1 (2001), pp.100-104
- Kh. R. Mamedov, ‘Uniqueness of Solution of the Scattering Theory with a Spectral Parameter in the Boundary Condition’, Math. Notes. 74, (1) (2003), pp.136-140
- E. M. Russakovskij, ‘Operator treatment of boundary problems with spectral parameters entering via polynomials in the boundary conditions’, Funct. Anal. Appl. 9, (1975); pp.358-359 (translation from Funkts. Anal. i Prilozh. 9, No.4, (1975), pp.91-92) (Russian, English)
- A. A. Shkalikov, ‘Boundary Value Problems for Ordinary Differential Equations with a Spectral Parameter in the Boundary Conditions’, Trudy Sem. İm. İ. G. Petrovsogo, V.9 (1983), pp.190- 229
- A. N. Tikhonov, A. A. Samarskii, Equations of Mathematical Physics (Dover Books on Physics and Chemistry, 1990)
- J. Walter, ‘Regular Eigenvalue Problems with Eigenvalue Parameter in the Boundary Conditions’, Math. Z., 133 (1973), pp. 301-312.