Asymptotics of the norming constants of the Sturm–Liouville problem
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2013), pp. 3-11.

Voir la notice de l'article provenant de la source Math-Net.Ru

We derive new asymptotic formulae for the norming constants of Sturm–Liouville problem, which generalize and make more precise previously known formulae, by taking into account the smooth dependence of norming constants on boundary conditions.
Keywords: norming constants, asymptotics of the solutions, asymptotics of spectral data.
Mots-clés : Sturm–Liouville problem
@article{UZERU_2013_3_a0,
     author = {T. N. Harutyunyan},
     title = {Asymptotics of the norming constants of the {Sturm{\textendash}Liouville} problem},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {3--11},
     publisher = {mathdoc},
     number = {3},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2013_3_a0/}
}
TY  - JOUR
AU  - T. N. Harutyunyan
TI  - Asymptotics of the norming constants of the Sturm–Liouville problem
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2013
SP  - 3
EP  - 11
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_2013_3_a0/
LA  - en
ID  - UZERU_2013_3_a0
ER  - 
%0 Journal Article
%A T. N. Harutyunyan
%T Asymptotics of the norming constants of the Sturm–Liouville problem
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2013
%P 3-11
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_2013_3_a0/
%G en
%F UZERU_2013_3_a0
T. N. Harutyunyan. Asymptotics of the norming constants of the Sturm–Liouville problem. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2013), pp. 3-11. http://geodesic.mathdoc.fr/item/UZERU_2013_3_a0/

[1] M.A. Naimark, Linear Differential Equations, Nauka, M., 1969 (in Russian) | MR

[2] B.M. Levitan, I.S. Sargsyan, Introduction to Spectral Theory, Nauka, M., 1970 (in Russian) | MR | Zbl

[3] V.A. Marchenko, The Sturm–Liouville Operators and Their Applications, Naukova Dumka, Kiev, 1977 (in Russian) | MR

[4] T.N. Harutyunyan, “The Dependence of the Eigenvalues of the Sturm–Liouville Problem on Boundary Conditions”, Matem. Vesnik, 60:4 (2008), 285–294 | MR | Zbl

[5] E.L. Isaacson, E. Trubowitz, “The Inverse Sturm–Liouville Problem. Part I”, Com. Pure Appl. Mathem., 36 (1983), 767–783 | DOI | MR | Zbl

[6] E.L. Isaacson, H.P. McKean, E. Trubowitz, “The Inverse Sturm–Liouville Problem. Part II”, Com. Pure Appl. Mathem., 37 (1984), 1–11 | DOI | MR | Zbl

[7] B.E. Dahlberg, E. Trubowitz, “The Inverse Sturm–Liouville Problem. Part III”, Com. Pure Appl. Mathem., 37 (1984), 255–267 | DOI | MR | Zbl

[8] J. Poshel, E. Trubowitz, Inverse Spectral Theory, Academic Press, N.-Y., 1987 | MR

[9] V.A. Yurko, Introduction to the Theory of Inverse Spectral Problems, Fizmatlit, M., 2007, 384 pp. (in Russian)

[10] V.V. Zikov, “On Inverse Sturm–Liouville Problems on a Finite Segment”, Izv. Akad. Nauk SSSR. Ser. Matem., 31:5 (1967), 965–976 (in Russian) | MR

[11] V.A. Marchenko, “Some Questions of the Theory of One-Dimensional Linear Differential Operators of the Second Order. Part I”, Trudy Mosk. Matem. Obsh., 1, 1952, 327–420 (in Russian) | MR

[12] L.A. Chudov, “The Inverse Sturm–Liouville Problem”, Matem. Sb., 25(67):3 (1949), 451–456 (in Russian) | MR | Zbl

[13] F. Atkinson, Discrete and Continuous Boundary Problems, Mir, M., 1968 (in Russian) | MR | Zbl

[14] T.N. Harutyunyan, M.S. Hovsepyan, “On the Solutions of the Sturm–Liouville Equation”, Matem. v Visshey Shkole, 1:3 (2005), 59–74 (in Russian)