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Resolvent Matrices in Degenerated Inner Product Spaces
Author(s) -
Woracek Harald
Publication year - 2000
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/(sici)1522-2616(200005)213:1<155::aid-mana155>3.0.co;2-2
Subject(s) - resolvent , mathematics , inner product space , product (mathematics) , algebra over a field , hilbert space , calculus (dental) , pure mathematics , geometry , medicine , dentistry
Nτ (z, w) := τ (z) − τ (w) z −w has ν negative squares. For notational convenience we assume that the function τ (z) ≡ ∞ belongs to N0. A matrix W (z) with the above property is called a u – resolvent matrix of S. The existence of a u – resolvent matrix is a consequence of Krein’s formula on the description of generalized resolvents. In [KW3] the element u was allowed to be a so – called generalized element, which leads to a natural characterization of those matrix functions W (z) which appear as