%0 Journal Article %T Matrix Sturm-Liouville operators with boundary conditions dependent on the spectral parameter %A Katar, Deniz %A Olgun, Murat %A Coskun, Cafer %J Journal of Nonlinear Sciences and Applications %D 2016 %V 9 %N 2 %@ ISSN 2008-1901 %F Katar2016 %X Let \(L\) denote the operator generated in\(L_2(\mathbb{R}_+;E)\) by the differential expression \[l(y) = -y'' + Q(x)y; \qquad x \in \mathbb{R}_+\]; and the boundary condition \((A_0 + A_1\lambda)Y' (0; \lambda) - (B_0 + B_1\lambda)Y (0; \lambda) = 0\) , where \(Q\) is a matrix-valued function and \(A_0; A_1; B_0; B_1\) are non-singular matrices, with \(A_0B_1 - A_1B_0 \neq 0\): In this paper, using the uniqueness theorems of analytic functions, we investigate the eigenvalues and the spectral singularities of \(L\). In particular, we obtain the conditions on q under which the operator \(L\) has a finite number of the eigenvalues and the spectral singularities. %9 journal article %R 10.22436/jnsa.009.02.09 %U http://dx.doi.org/10.22436/jnsa.009.02.09 %P 435--442 %0 Journal Article %T Difference equations of second order with spectral singularities %A M. Adivar %A E. Bairamov %J J. Math. Anal. Appl. %D 2003 %V 277 %F Adivar2003 %0 Book %T The inverse problem of scattering theory %A Z. S. Agranovich %A V. A. Marchenko %D 1963 %I Gordon and Breach %C New York %F Agranovich1963 %0 Journal Article %T Quadratic pencil of Schrödinger operators with spectral singularities: Discrete spectrum and principal functions %A E. Bairamov %A O. Cakar %A A. O. Celebi %J J. Math. Anal. Appl. %D 1997 %V 216 %F Bairamov1997 %0 Journal Article %T An eigenfunction expansion for a quadratic pencil of a Schrödinger operator with spectral singularities %A E. Bairamov %A O. Cakar %A A. M. Krall %J J. Differential Equations %D 1999 %V 151 %F Bairamov1999 %0 Journal Article %T Non-selfadjoint difference operators and Jacobi matrices with spectral singularities %A E. Bairamov %A O. Cakar %A A. M. Krall %J Math. Nachr. %D 2001 %V 229 %F Bairamov2001 %0 Journal Article %T Spectrum and spectral expansion for the non-selfadjoint discrete Dirac operators %A E. Bairamov %A A. O. Celebi %J Quart. J. Math. Oxford Ser. %D 1999 %V 50 %F Bairamov1999 %0 Journal Article %T The structure of the spectrum a system of difference equations %A E. Bairamov %A C. Coskun %J Appl. Math. Lett. %D 2005 %V 18 %F Bairamov2005 %0 Journal Article %T Non-selfadjoint singular Sturm-Liouville problems with boundary conditions dependent on the eigenparameter %A E. Bairamov %A S. Seyyidoğlu %J Abstr. Appl. Anal. %D 2010 %V 2010 %F Bairamov2010 %0 Journal Article %T Sets of uniqueness for functions regular in the unit circle %A L. Carleson %J Acta Math. %D 1952 %V 87 %F Carleson1952 %0 Journal Article %T An inverse problem for the matrix Schrödinger equation %A R. Carlson %J J. Math. Anal. Appl. %D 2002 %V 267 %F Carlson2002 %0 Journal Article %T Trace formulas and Borg-type theorems for matrix-valued Jacobi and Dirac finite difference operators %A S. Clark %A F. Gesztesy %A W. Renger %J J. Differential Equations %D 2005 %V 219 %F Clark2005 %0 Journal Article %T Principal functions of non-selfadjoint matrix Sturm-Liouville equations %A C. Coskun %A M. Olgun %J J. Comput. Appl. Math. %D 2011 %V 235 %F Coskun2011 %0 Journal Article %T Boundary value uniqueness theorems for analytic functions %A E. P. Dolzhenko %J Math. Notes %D 1979 %V 25 %F Dolzhenko1979 %0 Journal Article %T Uniqueness results for matrix-valued Schrödinger, Jacobi and Dirac-type operators %A F. Gesztesy %A A. Kiselev %A K. A. Makarov %J Math. Nachr. %D 2002 %V 239 %F Gesztesy2002 %0 Journal Article %T On Lebesgue's density theorem %A C. Góman %J Proc. Amer. Math. Soc. %D 1950 %V 1 %F Góman1950 %0 Journal Article %T Spectrum and spectral singularities of a quadratic pencil of a Schrödinger operator with a general boundary condition %A A. M. Krall %A E.Bairamov %A O. Cakar %J J. Differentional Equations %D 1999 %V 151 %F Krall1999 %0 Journal Article %T Spectral analysis of a non-selfadjoint discrete Schrödinger operators with spectral singularities %A A. M. Krall %A E. Bairamov %A O. Cakar %J Math. Nachr. %D 2001 %V 231 %F Krall2001 %0 Book %T Inverse Sturm-Liouville problems %A B. M. Levitan %D 1987 %I VSP %C Zeist %F Levitan1987 %0 Journal Article %T A differential operator with spectral singularities I, II %A V. E. Lyance %J Amer. Math. Soc. Transl., Amer. Math. Soc, Providence %D 1967 %V 60 %F Lyance1967 %0 Book %T Sturm-Liouville operators and applications %A V. A. Marchenko %D 1986 %I Birkhauser Verlag %C Basel %F Marchenko1986 %0 Journal Article %T A note on metric density of sets of real numbers %A N. F. G. Martin %J Proc. Amer. Math. Soc. %D 1960 %V 11 %F Martin1960 %0 Journal Article %T Investigation of the spectrum and the expansion in eigenfunctions of a non-selfadjoint operators of second order on a semi-axis %A M. A. Naimark %J Tr. Mosk. Mat. Obs. %D 1954 %V 3 %F Naimark 1954 %0 Book %T Linear differential operators II %A M. A. Naimark %D 1968 %I Ungar, NewYork, NY %C USA %F Naimark1968 %0 Journal Article %T Non-selfadjoint matrix Sturm-Liouville operators with spectral singularities %A M. Olgun %A C. Coskun %J Appl. Math. Comput. %D 2010 %V 216 %F Olgun2010 %0 Journal Article %T On a non-selfadjoint Schrödinger operator II %A B. S. Pavlov %J Prob. Math. Phys. %D 1967 %V 2 %F Pavlov 1967 %0 Journal Article %T On separation conditions for spectral components of a dissipative operator %A B. S. Pavlov %J Math. USSR-Izvestiya %D 1975 %V 39 %F Pavlov1975