The Krein Formula for Generalized Resolvents in Degenerated Inner Product Spaces |
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Authors: | Michael Kaltenbäck Harald Woracek |
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Affiliation: | Technische Universit?t Wien, Austria, AT
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Abstract: | Let S be a symmetric operator with defect index (1,1) in a Pontryagin space ℋ. The Krein formula establishes a bijective correspondence between the generalized resolvents of S and the set of Nevanlinna functions as parameters. We give an analogue of the Krein formula in the case that ℋ is a degenerated inner product space. The set of parameters is determined by a kernel condition. These results are applied to some classical interpolation problems with singular data. Received 3 February 1997; in revised form 9 June 1997 |
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Keywords: | 1991 Mathematics Subject Classification: 47B50 47B25 42A82 |
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