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

Studia Mathematica (1999)

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

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topKhatskevich, 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

top- [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. Zbl0082.07602
- [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). Zbl0484.47015
- [5] V. Khatskevich, Some global properties of fractional linear transformations, in: Oper. Theory Adv. Appl. 73, Birkhäuser, Basel, 1994, 355-361. Zbl0832.47029
- [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. Zbl0855.34068
- [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] 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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