Geodesic
Spectral analysis of higher-order differential operators with discontinuity conditions at an interior point
Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 63 (2017) no. 2, pp. 362-372 
V. A. Yurko. Spectral analysis of higher-order differential operators with discontinuity conditions at an interior point. Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 63 (2017) no. 2, pp. 362-372. http://geodesic.mathdoc.fr/item/CMFD_2017_63_2_a7/
@article{CMFD_2017_63_2_a7,
     author = {V. A. Yurko},
     title = {Spectral analysis of higher-order differential operators with discontinuity conditions at an interior point},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {362--372},
     year = {2017},
     volume = {63},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2017_63_2_a7/}
}
TY  - JOUR
AU  - V. A. Yurko
TI  - Spectral analysis of higher-order differential operators with discontinuity conditions at an interior point
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2017
SP  - 362
EP  - 372
VL  - 63
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMFD_2017_63_2_a7/
LA  - ru
ID  - CMFD_2017_63_2_a7
ER  - 
%0 Journal Article
%A V. A. Yurko
%T Spectral analysis of higher-order differential operators with discontinuity conditions at an interior point
%J Contemporary Mathematics. Fundamental Directions
%D 2017
%P 362-372
%V 63
%N 2
%U http://geodesic.mathdoc.fr/item/CMFD_2017_63_2_a7/
%G ru
%F CMFD_2017_63_2_a7

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Higher-order differential operators on a finite interval with jump conditions inside the interval are studied. Properties of spectral characteristics are obtained, and completeness and expansion theorems are proved for this class of operators.

[1] B. M. Levitan, I. S. Sargsyan, Introduction to Spectral Theory, Nauka, Moscow, 1970 (in Russian)

[2] O. N. Litvinenko, V. I. Soshnikov, Theory of Nonhomogeneous Lines and Their Applications in Radio Engineering, Sov. radio, Moscow, 1964 (in Russian)

[3] V. P. Meshchanov and A. L. Feldstein, Automatic Design of Directional Couplers, Svyaz', Moscow, 1980 (in Russian)

[4] M. A. Naimark, Linear Differential Operators, Nauka, Moscow, 1969 (in Russian) | MR

[5] V. A. Yurko, “On boundary-value problems with discontinuity conditions inside the interval”, Diff. uravn., 36:8 (2000), 1139–1140 (in Russian) | MR | Zbl

[6] Amirov R., Ozkan A., “Discontinuous Sturm–Liouville problems with eigenvalue dependent boundary conditions”, Math. Phys. Anal. Geom., 17:3–4 (2014), 483–491 | MR | Zbl

[7] Anderssen R. S., “The effect of discontinuities in density and shear velocity on the asymptotic overtone structure of torsional eigenfrequencies of the Earth”, Geophys. J. R. Astr. Soc., 50 (1997), 303–309 | DOI

[8] Beals R., Deift P., Tomei C., Direct and inverse scattering on the line, Am. Math. Soc., Providence, 1988 | MR | Zbl

[9] Freiling G., Yurko V. A., Inverse Sturm–Liouville problems and their applications, NOVA Science Publishers, New York, 2001 | MR | Zbl

[10] Hald O. H., “Discontinuous inverse eigenvalue problems”, Commun. Pure Appl. Math., 37 (1984), 539–577 | DOI | MR | Zbl

[11] Krueger R. J., “Inverse problems for nonabsorbing media with discontinuous material properties”, J. Math. Phys., 23:3 (1982), 396–404 | DOI | MR | Zbl

[12] Lapwood F. R., Usami T., Free oscillations of the Earth, Cambridge University Press, Cambridge, 1981 | Zbl

[13] Shepelsky D. G., “The inverse problem of reconstruction of the medium's conductivity in a class of discontinuous and increasing functions”, Adv. Sov. Math., 19 (1994), 209–231 | MR

[14] Yurko V. A., “Integral transforms connected with discontinuous boundary value problems”, Integral Transforms Spec. Funct., 10:2 (2000), 141–164 | DOI | MR | Zbl

[15] Yurko V. A., Method of spectral mappings in the inverse problem theory, VSP, Utrecht, 2002 | MR