Wave model of the Sturm–Liouville operator on an interval
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 48, Tome 471 (2018), pp. 225-260 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper we construct the wave functional model of a symmetric restriction of the regular Sturm–Liouville operator on an interval. The model is based upon the notion of the wave spectrum and is constructed according to an abstract scheme which was proposed earlier. The result of the construction is a differential operator of the second order on an interval, which differs from the original operator only by a simple transformation.
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S. A. Simonov. Wave model of the Sturm–Liouville operator on an interval. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 48, Tome 471 (2018), pp. 225-260. http://geodesic.mathdoc.fr/item/ZNSL_2018_471_a13/

[1] M. I. Belishev, “K zadache Katsa o vosstanovlenii formy oblasti po spektru zadachi Dirikhle”, Zap. nauchn. semin LOMI, 173, 1988, 30–41 | MR | Zbl

[2] M. I. Belishev, M. N. Demchenko, “Dinamicheskaya sistema s granichnym upravleniem, assotsiirovannaya s simmetricheskim poluogranichennym operatorom”, Zap. nauchn. semin POMI, 409, 2012, 17–39 | MR

[3] M. I. Belishev, S. A. Simonov, “Volnovaya model operatora Shturma–Liuvillya na poluosi”, Algebra i analiz, 29:2 (2017), 3–33 | MR

[4] G. Birkgof, Teoriya reshetok, Nauka, Moskva, 1984

[5] M. Sh. Birman, M. Z. Solomyak, Spektralnaya teoriya samosopryazhennykh operatorov v gilbertovom prostanstve, LGU, 1980

[6] M. I. Vishik, “Ob obschikh kraevykh zadachakh dlya ellipticheskikh differentsialnykh uravnenii”, Tr. Moskovskogo matem. obsch., 1, 1952, 187–246 | Zbl

[7] D. Kelli, Obschaya topologiya, Nauka, Moskva, 1981

[8] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, Nauka, Moskva, 1989

[9] A. N. Kochubei, “O rasshireniyakh simmetricheskikh operatorov i simmetricheskikh binarnykh otnoshenii”, Matem. zametki, 17:1 (1975), 41–48 | MR | Zbl

[10] M. A. Naimark, Lineinye differentsialnye operatory, Nauka, Moskva, 1969

[11] A. V. Shtraus, “Funktsionalnye modeli i obobschennye spektralnye funktsii simmetricheskikh operatorov”, Algebra i analiz, 10:5 (1998), 1–76 | MR | Zbl

[12] M. I. Belishev, “Boundary control in reconstruction of manifolds and metrics (the BC method)”, Inverse Problems, 13:5 (1997), 1–45 | DOI | MR

[13] M. I. Belishev, “Recent progress in the boundary control method”, Inverse Problems, 23:5 (2007), 1–67 | DOI | MR

[14] M. I. Belishev, “A unitary invariant of a semi-bounded operator in reconstruction of manifolds”, J. Operator Theory, 69:2 (2013), 299–326 | DOI | MR | Zbl

[15] M. I. Belishev, M. N. Demchenko, “Elements of noncommutative geometry in inverse problems on manifolds”, J. Geom. Phys., 78 (2014), 29–47 | DOI | MR | Zbl

[16] V. A. Derkach, M. M. Malamud, “The extension theory of Hermitian operators and the moment problem”, J. Math. Sci., 73:2 (1995), 141–242 | DOI | MR | Zbl

[17] J. M. Kim, “Compactness in $\mathcal B(X)$”, J. Math. Anal. Appl., 320 (2006), 619–631 | DOI | MR | Zbl

[18] V. Ryzhov, “A general boundary value problem and its Weyl function”, Opuscula Math., 27:2 (2007), 305–331 | MR | Zbl

[19] S. A. Simonov, “Wave model of the regular Sturm–Liouville operator”, Proceedings of 2017 Days on Diffraction, 2017, 300–303; arXiv: 1801.02011