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

V. Khatskevich

Studia Mathematica (1999)

  • Volume: 137, Issue: 2, page 169-175
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Khatskevich, V.. "Generalized fractional linear transformations: convexity and compactness of the image and the pre-image; applications.." Studia Mathematica 137.2 (1999): 169-175. <http://eudml.org/doc/216682>.

@article{Khatskevich1999,
abstract = {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.},
author = {Khatskevich, V.},
journal = {Studia Mathematica},
keywords = {generalized fractional linear multivalued transformations; plus-operators in Krein spaces; image; pre-image; weak operator topology; parabolic evolution problem},
language = {eng},
number = {2},
pages = {169-175},
title = {Generalized fractional linear transformations: convexity and compactness of the image and the pre-image; applications.},
url = {http://eudml.org/doc/216682},
volume = {137},
year = {1999},
}

TY - JOUR
AU - Khatskevich, V.
TI - Generalized fractional linear transformations: convexity and compactness of the image and the pre-image; applications.
JO - Studia Mathematica
PY - 1999
VL - 137
IS - 2
SP - 169
EP - 175
AB - 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.
LA - eng
KW - generalized fractional linear multivalued transformations; plus-operators in Krein spaces; image; pre-image; weak operator topology; parabolic evolution problem
UR - http://eudml.org/doc/216682
ER -

References

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  1. [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. [2] L. Cesari, Asymptotic Behavior and Stability Problems in Ordinary Differential Equations, Springer, 1959. Zbl0082.07602
  3. [3] V. Khatskevich, On fixed points of generalized fractional linear transformations, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), 1130-1141 (in Russian). 
  4. [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). Zbl0484.47015
  5. [5] V. Khatskevich, Some global properties of fractional linear transformations, in: Oper. Theory Adv. Appl. 73, Birkhäuser, Basel, 1994, 355-361. Zbl0832.47029
  6. [6] V. Khatskevich and V. Shul'man, Operator fractional linear transformations: convexity and compactness of image; applications, Studia Math. 116 (1995), 189-195. 
  7. [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. Zbl0855.34068
  8. [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. Zbl0868.34046
  9. [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. [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. [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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