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1999 | 137 | 2 | 169-175
Tytuł artykułu

Generalized fractional linear transformations: convexity and compactness of the image and the pre-image; applications.

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Abstrakty
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The convexity and compactness in the weak operator topology of the image and pre-image of a generalized fractional linear transformation is established. As an application the exponential dichotomy of solutions to evolution problems of the parabolic type is proved.
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  • Department of Applied Mathematics, Ort Braude College, P.O. Box 78, 21982 Karmiel, Israel, victor_kh@hotmail.com
Bibliografia
  • [1] T. Ya. Azizov and I. S. Ǐokhvidov, Foundations of the Theory of Linear Operators in Spaces with Indefinite Metric, Nauka, Moscow, 1986 (in Russian).
  • [2] L. Cesari, Asymptotic Behavior and Stability Problems in Ordinary Differential Equations, Springer, 1959.
  • [3] V. Khatskevich, On fixed points of generalized fractional linear transformations, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), 1130-1141 (in Russian).
  • [4] V. Khatskevich, On the symmetry of properties of a plus-operator and its adjoint operator, Funct. Analysis (Ulyanovsk) 14 (1980), 177-186 (in Russian).
  • [5] V. Khatskevich, Some global properties of fractional linear transformations, in: Oper. Theory Adv. Appl. 73, Birkhäuser, Basel, 1994, 355-361.
  • [6] V. Khatskevich and V. Shul'man, Operator fractional linear transformations: convexity and compactness of image; applications, Studia Math. 116 (1995), 189-195.
  • [7] V. Khatskevich and L. Zelenko, Indefinite metrics and dichotomy of solutions to linear differential equations in Hilbert spaces, Chinese J. Math. 2 (1996), 99-112.
  • [8] V. Khatskevich and L. Zelenko, The fractional-linear transformations of the operator ball and dichotomy of solutions to evolution equations, in: Contemp. Math. 204, Amer. Math. Soc., 1997, 149-154.
  • [9] V. A. Khatskevich and A. V. Sobolev, On definite invariant subspaces and spectral structure of focused plus-operators, Funktsional. Anal. i Prilozhen. 15 (1981), no. 1, 84-85 (in Russian).
  • [10] M. A. Krasnosel'skiĭ and A. V. Sobolev, On cones of finite rank, Dokl. Akad. Nauk SSSR 225 (1975), 1256-1259 (in Russian).
  • [11] M. G. Kreĭn and Yu. L. Shmul'yan, On fractional-linear transformations with operator coefficients, Mat. Issled. Kishinev 2 (1967), 64-96 (in Russian).
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