Glasnik matematički, Vol. 35 No. 1, 2000.
Original scientific paper
Operator representations of N+ - functions in a model Krein space L^2_sigma
Andreas Fleige
Abstract
We introduce the class N∞+ of all complex functions Q such that Q+(z) := z · Q(z) is a Nevalinna function. If 0 ∈ D(Q) and limy → ∞ Q(iy) = 0 we prove an integral representation Q(z) = ∫-∞∞ 1/(t-z) dσ(t) with a nonmonotonic function σ. If in particular Q+ is an R1-function we obtain an operator representation Q(z) = [(A - z) -1 F-, F-]σ with a selfadjoint, nonnegative and boundedly invertible multiplication operator A in the model Krein space (Lσ², [.,.]σ) and an element F- ∈ Lσ². The nonsingularity of the critical point infinity of A makes this representation unique up to a Krein space isomorphism.
Keywords
Hrčak ID:
4863
URI
Publication date:
1.6.2000.
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