Ismailov, Zameddin I.; Ipek, Pembe Spectrums of solvable pantograph type delay differential operators for first order. (English) Zbl 1358.34071 Anastassiou, George A. (ed.) et al., Computational analysis. AMAT, Ankara, May 2015. Selected contributions presented at the 3rd international conference on applied mathematics and approximation theory, Ankara, Turkey, May 28–31, 2015. Cham: Springer (ISBN 978-3-319-28441-5/hbk; 978-3-319-28443-9/ebook). Springer Proceedings in Mathematics & Statistics 155, 299-311 (2016). Summary: Based on Vishik’s method on the description of solvable extensions of a densely defined operator all solvable extensions of the minimal operator generated by some delay differential-operator expression for first order in the Hilbert space of vector-functions at finite interval are described. Later on, the structure of spectrum of these extensions is surveyed.For the entire collection see [Zbl 1348.65006]. Cited in 1 Document MSC: 34K08 Spectral theory of functional-differential operators Keywords:Vishik’s method × Cite Format Result Cite Review PDF Full Text: DOI References: [1] A.A. Dezin, General Problems in the Theory of Boundary Value Problems (Nauka, Moscow, 1980) [in Russian] · Zbl 0494.35084 [2] L. Edelstein-Keshet, Mathematical Models in Biology (McGraw-Hill, New York, 1988) · Zbl 0674.92001 [3] T. Erneux, An Introduction to Delay Differential Equations with Applications to the Life Sciences (Springer, New York, 2011) [4] J.K. Hale, S.M.V. Lunel, Introduction to Functional Differential Equations (Springer, New York, 1993) · Zbl 0787.34002 · doi:10.1007/978-1-4612-4342-7 [5] Z.I. Ismailov, Description of all regular operators (of solvable extensions) for first-order differential equations in a Hilbert space. Ukr. Math. J. 37 (4), 285–287 (1985) · Zbl 0611.34057 [6] B.K. Kokebaev, M. Otelbaev, A.N. Shynybekov, On the theory of contraction and extension of operators. I. Izv. Akad. Nauk Kazakh. SSR Ser. Fiz.-Mat. 5, 24–26 (1982) [in Russian] · Zbl 0509.47054 [7] B.K. Kokebaev, M. Otelbaev, A.N. Shynybekov, On the theory of contraction and extension of operators. II. Izv. Akad. Nauk Kazakh. SSR Ser. Fiz.-Mat. 110, 24–26 (1983) [in Russian] · Zbl 0599.47010 [8] B.K. Kokebaev, M. Otelbaev, A.N. Shynybekov, On questions of extension and restriction of operator. Sov. Math. Dokl. 28 (1), 259–262 (1983) · Zbl 0544.47003 [9] S.G. Krein, Linear Differential Equations in Banach Space, vol. 29. Translations of Mathematical Monographs (American Mathematical Society, Providence, RI, 1971) [10] J.R. Ockendon, A.B. Tayler, The dynamics of a current collection system for an electric locomotive. Proc. R. Soc. Lond. Ser. A 322, 447–468 (1971) · doi:10.1098/rspa.1971.0078 [11] M. Otelbaev, A.N. Shynybekov, Well-posed problems of Bitsadze-Samarskii type. Sov. Math. Dokl. 26 (1), 157–161 (1983) · Zbl 0522.47055 [12] N.I. Pivtorak, Solvable boundary value problems for an operator-differential equations for parabolic type. Akad. Nauk Ukr. SSR Inst. Mat. Kiev 9, 104–107 (1985) [in Russian] · Zbl 0582.34074 [13] H. Smith, Applied Delay Differential Equations (Springer, New York, 2009) [14] M.I. Vishik, On linear boundary problems for differential equations. Doklady Akad. Nauk SSSR (N.S.) 65, 785–788 (1949) [15] M.I. Vishik, On general boundary problems for elliptic differential equations. Am. Math. Soc. Transl. II 24, 107–172 (1963) · Zbl 0131.32301 · doi:10.1090/trans2/024/06 [16] J. von Neumann, Allgemeine eigenwerttheorie Hermitescher funktionaloperatoren. Math. Ann. 102, 49–131 (1929–1930) · JFM 55.0824.02 · doi:10.1007/BF01782338 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.