REPRESENTATION THEOREMS FOR INDEFINITE QUADRATIC FORMS REVISITED

REPRESENTATION THEOREMS FOR INDEFINITE QUADRATIC FORMS REVISITED

The first and second representation theorems for sign-indefinite, not necessarily semi-bounded quadratic forms are revisited. New and straightforward proofs of these theorems are given. A number of necessary and sufficient conditions for the second representation theorem to hold are obtained. A new...

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Bibliographic Details
Published in:Mathematika Vol. 59; no. 1; pp. 169 - 189
Main Authors: Grubišić, Luka, Kostrykin, Vadim, Makarov, Konstantin A., Veselić, Krešimir
Format: Journal Article
Language:English
Published: London, UK London Mathematical Society 01-01-2013
Subjects:
15A63
46C20 (secondary)
47A07
47A55 (primary)
15A63
47A07
46C20 (secondary)
47A55 (primary)
Online Access:Get full text
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Summary:The first and second representation theorems for sign-indefinite, not necessarily semi-bounded quadratic forms are revisited. New and straightforward proofs of these theorems are given. A number of necessary and sufficient conditions for the second representation theorem to hold are obtained. A new simple and explicit example of a self-adjoint operator for which the second representation theorem fails to hold is also provided.
ISSN:0025-5793
2041-7942
DOI:10.1112/S0025579312000125