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Hyponormal differential operators with discrete spectrum

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Języki publikacji
EN
Abstrakty
EN
In this work, we first describe all the maximal hyponormal extensions of a minimal operator generated by a linear differential-operator expression of the first-order in the Hilbert space of vector-functions in a finite interval. Next, we investigate the discreteness of the spectrum and the asymptotical behavior of the modules of the eigenvalues for these maximal hyponormal extensions.
Rocznik
Strony
79--94
Opis fizyczny
Bibliogr. 21 poz.
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autor
Bibliografia
  • [1] Yu.M. Berezanskii, Expansions in eigenfunctions of self – adjoint operators, Amer. Math. Soc., Providence, RI, 17, 1968.
  • [2] V.M. Bruk, Some problems of the spectral theory of the linear differential equations for first order with unbounded operator coefficient, Functional Analysis and Its Applications. Moscow 1 (1973), 15–25 [in Russian].
  • [3] E.A. Coddington, Extension theory of formally normal and symmetric subspaces, Mem. Amer. Math. Soc. 134 (1973), 1–80.
  • [4] N. Dunford, J.T. Schwartz, Linear operators, p.I, Interscience Publishers, New York, London, 1958.
  • [5] I.C. Gohberg, M.G. Krein, Introduction to the theory of linear non-self-adjoint operators, Amer. Math. Soc., Providence, RI, 1969.
  • [6] M.L. Gorbachuk, Self-adjoint boundary value problems for the differential equations for second order with the unbounded operator coefficient, Functional Analysis and Its Applications 5 (1971), 10–21 [in Russian].
  • [7] V.I. Gorbachuk, M.L. Gorbachuk, Boundary value problems for operator-differential equations, Kluwer Academic Publisher, Dordrecht, 1991.
  • [8] P.R. Halmos, A Hilbert Space Problem Book, Van Nostrad, Princeton, New Jersey, 1967.
  • [9] E. Hille, R.S. Phillips, Functional Analysis and Semi-Groups, Amer. Math. Soc., Providence, RI, 31, 1957.
  • [10] Z.I. Ismailov, H. Karatash, Some necessary conditions for the normality of differential operators, Doklady Mathematics, Birmingham (Alabama), USA, 62 (2000) 2, 277–279.
  • [11] Z.I. Ismailov, On the normality of first-order differential operators, Bull. Polish Acad. Sci. Math. 51 (2003) 2, 139–145.
  • [12] Z.I. Ismailov, Discreteness of the spectrum of first order normal differential operators, Doklady Mathematics, Birmingham (Alabama), USA, 57 (1998) 1, 32-33.
  • [13] Z.I. Ismailov, Compact inverses of first-order normal differential operators, J. Math. Anal. Appl. 320 (2006), 266–278.
  • [14] S.G. Krein, Linear differential equations in Banach Spaces, Amer. Math. Soc. Providence, RI, 1971.
  • [15] F.G. Maksudov, Z.I. Ismailov, Normal boundary value problems for the first-order differential equations, Doklady Mathematics, Birmingham (Alabama), USA, 54 (1996) 2, 659–661.
  • [16] F.G. Maksudov, Z.I. Ismailov, One necessary condition for normality of differential operators, Doklady Mathematics, Birmingham (Alabama), USA, 59 (1999) 3, 422–424.
  • [17] C.R. Putnam, Spectra of polar factors of hyponormal operators, Trans. Amer. Math. Soc. 188 (1974), 419–428.
  • [18] J.G. Stampfli, Hyponormal operators, Pacific J. Math. 12 (1992), 1453–1458.
  • [19] J.G. Stampfli, Hyponormal operators and Spectral density, Trans. Amer. Math. Soc. 117 (1965), 469–476.
  • [20] L.R. Williams, Quasisimilarity and hyponormal operators, J. Operator Theory 5 (1981), 127–139.
  • [21] D. Xia, Spectral Theory of Hyponormal Operators, Birkhäuser Verlag, Boston, 1983.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHT-0002-0016
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