Glasnik Matematicki, Vol. 35, No.1 (2000), 149-160.
A CLASS OF 2 × 2 MATRIX FUNCTIONS
Heinz Langer and Annemarie Luger
Institut fur Analysis und Technische Mathematik,
Technische Universitat Wien, A-1040 Wien, Austria
e-mail: hlanger@mail.zserv.tuwien.ac.at
Abstract. For a special class 2 × 2-matrix
functions Ω
operator representations of
Ω(z)
and Ω^(z)
:= - Ω(z) -1
by means of self-adjoint linear relations A and
A^ in a Krein space
K are given.
Since A^ is a 2-dimensional perturbation of
A, results of Langer, Markus and Matsaev imply that
"singularities of positive type" of
Ω remain
singularities of positive type of
Ω^
with the possible exception of isolated points which have a
"finite negative index".
1991 Mathematics Subject Classification.
47B50, 30E99.
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