Search results for "Krein space"

showing 2 items of 2 documents

Representation Theorems for Indefinite Quadratic Forms Revisited

2010

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.

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)
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Generalized Riesz systems and orthonormal sequences in Krein spaces

2018

We analyze special classes of bi-orthogonal sets of vectors in Hilbert and in Krein spaces, and their relations with generalized Riesz systems. In this way, the notion of the first/second type sequences is introduced and studied. We also discuss their relevance in some concrete quantum mechanical system driven by manifestly non self-adjoint Hamiltonians.

Statistics and ProbabilityPure mathematics46N50 81Q12FOS: Physical sciencesGeneral Physics and AstronomyStatistical and Nonlinear PhysicsMathematical Physics (math-ph)Mathematics::Spectral TheoryRiesz basisBiorthogonal sequenceModeling and SimulationPT -symmetric HamiltonianKrein spaceOrthonormal basisSettore MAT/07 - Fisica MatematicaMathematical PhysicsMathematicsJournal of Physics A: Mathematical and Theoretical
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