On an evolutionary dynamical system of the first order with boundary control
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 49, Tome 483 (2019), pp. 41-54 Cet article a éte moissonné depuis la source Math-Net.Ru

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The work is carried out as part of a program to construct a new functional (so-called wave) model of symmetric operators. It is shown that an abstract evolutionary dynamic system of the first order (w.r.t. time) with boundary control, which is determined by a symmetric operator $L_0:{\mathscr H}\to{\mathscr H}$, is controllable if and only if $L_0$ has no maximal symmetric parts in ${\mathscr H}$.
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M. I. Belishev; S. A. Simonov. On an evolutionary dynamical system of the first order with boundary control. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 49, Tome 483 (2019), pp. 41-54. http://geodesic.mathdoc.fr/item/ZNSL_2019_483_a2/

[1] N. I. Akhiezer, I. M. Glazman, Teoriya lineinykh operatorov v gilbertovom prostranstve, Nauka, M., 1966 | MR

[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

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

[4] M. I. Belishev, S. A. Simonov, “Volnovaya model metricheskogo prostranstva s meroi”, Matem. sb., 2019

[5] M. I. Belishev, S. A. Simonov, “Volnovaya model metricheskikh prostranstv”, Funkts. analiz pril., 53:2 (2019), 3–10 | DOI | MR | Zbl

[6] M. Sh. Birman, M. Z. Solomyak, Spektralnaya teoriya samosopryazhennykh operatorov v gilbertovom prostranstve, Lan, S.-Peterburg–M.–Krasnodar, 2010

[7] V. A. Derkach, M. M. Malamud, Teoriya rasshirenii simmetricheskikh operatorov i granichnye zadachi, PRATsI Institutu matematiki NAN Ukraini. Matematika ta ii zastosuvannya, 104, 2017

[8] S. G. Krein, Lineinye differentsialnye uravneniya v banakhovom prostranstve, Nauka, M., 1967

[9] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki, v. 2, Mir, M., 1978

[10] 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