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Representation Theorems for Indefinite Quadratic Forms Revisited
Krešimir VeselićLuka GrubišićVadim KostrykinKonstantin A. Makarovsubject
Pure mathematicsGeneral MathematicsFOS: Physical sciencesMathematical proofDirac operator01 natural sciencesMathematics - Spectral Theorysymbols.namesakeOperator (computer programming)Simple (abstract algebra)0103 physical sciencesFOS: Mathematics0101 mathematicsSpectral Theory (math.SP)Mathematical PhysicsMathematicsRepresentation theorem010102 general mathematicsRepresentation (systemics)Mathematical Physics (math-ph)16. Peace & justice47A07 47A55 15A63 46C20Functional Analysis (math.FA)Mathematics - Functional AnalysisTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESsymbolsIndefinite quadratic forms ; representation theorems ; perturbation theory ; Krein spaces ; Dirac operator010307 mathematical physicsPerturbation theory (quantum mechanics)description
The first and second representation theorems for sign-indefinite, not necessarily semi-bounded quadratic forms are revisited. New straightforward proofs of these theorems are given. A number of necessary and sufficient conditions ensuring the second representation theorem to hold is proved. A new simple and explicit example of a self-adjoint operator for which the second representation theorem does not hold is also provided.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2010-03-09 |