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@article{AUM_2021_75_2_a0, author = {Allahverdiev, Bilender and Tuna, Huseyin}, title = {On extensions of matrix-valued {Hahn{\textendash}Sturm{\textendash}Liouville} operators}, journal = {Annales Universitatis Mariae Curie-Sk{\l}odowska. Mathematica }, pages = {1--12}, publisher = {mathdoc}, volume = {75}, number = {2}, year = {2021}, language = {en}, url = {http://geodesic.mathdoc.fr/item/AUM_2021_75_2_a0/} }
TY - JOUR AU - Allahverdiev, Bilender AU - Tuna, Huseyin TI - On extensions of matrix-valued Hahn–Sturm–Liouville operators JO - Annales Universitatis Mariae Curie-Skłodowska. Mathematica PY - 2021 SP - 1 EP - 12 VL - 75 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/AUM_2021_75_2_a0/ LA - en ID - AUM_2021_75_2_a0 ER -
%0 Journal Article %A Allahverdiev, Bilender %A Tuna, Huseyin %T On extensions of matrix-valued Hahn–Sturm–Liouville operators %J Annales Universitatis Mariae Curie-Skłodowska. Mathematica %D 2021 %P 1-12 %V 75 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/AUM_2021_75_2_a0/ %G en %F AUM_2021_75_2_a0
Allahverdiev, Bilender; Tuna, Huseyin. On extensions of matrix-valued Hahn–Sturm–Liouville operators. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 75 (2021) no. 2, pp. 1-12. http://geodesic.mathdoc.fr/item/AUM_2021_75_2_a0/
[1] Allakhverdiev, B. P., On extensions of symmetric Schrodinger operators with a matrix potential, Izv. Ross. Akad. Nauk Ser. Mat. 59 (1995), 19–54 (Russian); English translation Izv. Math. 59 (1995), 45–62.
[2] Allahverdiev, B. P., Tuna, H., A spectral expansion for Hahn–Sturm–Liouville equation on the whole line, Folia Math. 23 (1) (2021), 3–19.
[3] Allahverdiev, B. P., Tuna, H., Spectral theory of singular Hahn difference equation of the Sturm–Liouville type, Commun. Math. 28 (1) (2020), 13–25.
[4] Allahverdiev, B. P., Tuna, H., A representation of the resolvent operator of singular Hahn–Sturm–Liouville problem, Numer. Funct. Anal. Optim. 41 (4) (2020), 413–431.
[5] Allahverdiev, B. P., Tuna, H., Extensions of the matrix-valued q-Sturm–Liouville operators, Turkish J. Math. 45 (2021), 1479–1494.
[6] Annaby, M. H., Hamza, A. E., Aldwoah, K. A., Hahn difference operator and associated Jackson–Norlund integrals, J. Optim. Theory Appl. 154 (2012), 133–153.
[7] Annaby, M. H., Hamza, A. E., Makharesh, S. D., A Sturm–Liouville theory for Hahn difference operator, in: Xin Li, Zuhair Nashed (Eds.), Frontiers of Orthogonal Polynomials and q-Series, World Scientific, Singapore, 2018, 35–84.
[8] Atkinson, F. V., Discrete and Continuous Boundary Problems, Acad. Press Inc., New York, 1964.
[9] Aygar, Y., Bohner, M., Spectral analysis of a matrix-valued quantum-difference operator, Dynam. Syst. Appl. 25 (2016), 1–9.
[10] Bairamov, E., Cebesoy, S¸., Spectral singularities of the matrix Schrodinger equations, Hacettepe J. Math. Stat. 45 (4) (2016), 1007–1014.
[11] Bastard, G., Brum, J. A., Electronic states in semi conductor heterostructures, IEEE J. Quantum Electron. 22 (1986), 1625–1644.
[12] Bastard, G., Wave Mechanics Applied to Semi Conductor Hetero Structures, Paris, ´Editions de Physique, 1989.
[13] Beals, R., Henkin, G. M., Novikova, N. N., The inverse boundary problem for the Rayleigh system, J. Math. Phys. 36 (12) (1965), 6688–6708.
[14] Bondarenko, N., Spectral analysis for the matrix Sturm–Liouville operator on a finite interval, Tamkang J. Math. 42 (3) (2011), 305–327.
[15] Boutet de Monvel, A., Shepelsky, D., Inverse scattering problem for anisotropic media, J. Math. Phys. 36 (7) (1995), 3443–3453.
[16] Bruk, V. M., On a class of boundary-value problems with a spectral parameter in the boundary conditions, Mat. Sb. (N.S.) 100 (1976), 210–216 (Russian).
[17] Calkin, J. W., Abstract symmetric boundary conditions, Trans. Amer. Math. Soc. 45 (3) (1939), 369–442.
[18] Chabanov, V. M., Recovering the M-channel Sturm–Liouville operator from M + 1 spectra, J. Math. Phys. 45 (11) (2004), 4255–4260.
[19] Gorbachuk, M. L., On spectral functions of a second order differential operator with operator coefficients, Ukrain. Mat. Zhurnal 18 (2) (1966), 3–21 (Russian); English translation American Mathematical Society Translations: Ser. 2 72 (1968), 177–202.
[20] Gorbachuk, M. L., Gorbachuk, V. I., Kochubei, A. N., The theory of extensions of symmetric operators and boundary-value problems for differential equations, Ukrain. Mat. Zhurnal 41 (1989), 1299–1312 (Russian); English translation Ukrain. Math. J. 41 (1989), 1117–1129.
[21] Gorbachuk, M. L., Gorbachuk, V. I., Boundary Value Problems for Operator Differential Equations, Naukova Dumka, Kiev, 1984 (Russian); English translation Birkhauser Verlag, 1991.
[22] Hahn, W., Uber Orthogonalpolynome, die q-Differenzengleichungen genugen, Math. Nachr. 2 (1949), 4–34 (German).
[23] Hahn, W., Ein Beitrag zur Theorie der Orthogonalpolynome, Monatsh. Math. 95 (1983), 19–24 (German).
[24] Kochubei, A. N., Extensions of symmetric operators and symmetric binary relations, Mat. Zametki 17 (1975), 41–48 (Russian); English translation Math. Notes 17 (1975), 25–28.
[25] Krall, A. M., Hilbert Space, Boundary Value Problems and Orthogonal Polynomials, Birkhauser Verlag, Basel–Boston–Berlin, 2002.
[26] Krein, M. G., On the indeterminate case of the Sturm–Liouville boundary value problem in the interval (0;1), Izvest. Akad. Nauk SSSR. Ser. Mat. 16 (1952), 292–324 (Russian).
[27] Naimark, M. A., Linear Differential Operators, 2nd ed., Nauka, Moscow, 1969 (Russian); English translation of 1st. ed., Part I, Part II, Frederick Ungar Publishing Co., New York, 1967, 1968.
[28] Maksudov, F. G., Allakhverdiev, B. P., On the extensions of Schr¨odinger operators with a matrix potentials, Doklady Akad. Nauk 332 (1) (1993), 18–20 (Russian); English translation Russian Acad. Sci. Doklady Math. 48 (2) (1994), 240–243.
[29] Malamud, M. M., Mogilevskii, V. I., On extensions of dual pairs of operators, Dopov. Nats. Akad. Nauk Ukr. 11 (1997), 30–37.
[30] Mogilevskii, V. I., On proper extensions of a singular differential operator in a space of vector functions, Dopov. Akad. Nauk Ukraini 9 (1994), 29–33 (Russian).
[31] Rofe-Beketov, F. S., Self-adjoint extensions of differential operators in a space of vector valued functions, Dokl. Akad. Nauk SSSR 184 (1969), 1034–1037 (Russian); English translation Soviet Math. Dokl. 10 (1969), 188–192.
[32] Shi, Y., Weyl–Titchmarsh theory for a class of discrete linear Hamiltonian systems, Linear Algebra Appl. 416 (2006), 452–519.
[33] von Neumann, J., Allgemeine Eigenwertheorie Hermitischer Functionaloperatoren, Math. Annal. 102 (1929), 49–131 (German).
[34] Yurko, V., Inverse problems for the matrix Sturm–Liouville equation on a finite interval, Inverse Problems 22 (2006), 1139–1149.
[35] Zettl, A., Sturm–Liouville Theory, American Mathematical Society, Providence, RI, 2005.