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On a generalisation of Krein's example

2017

We generalise a classical example given by Krein in 1953. We compute the difference of the resolvents and the difference of the spectral projections explicitly. We further give a full description of the unitary invariants, i.e., of the spectrum and the multiplicity. Moreover, we observe a link between the difference of the spectral projections and Hankel operators.

Pure mathematicsClassical exampleApplied Mathematics010102 general mathematicsFOS: Physical sciencesMultiplicity (mathematics)Mathematical Physics (math-ph)01 natural sciencesUnitary stateFunctional Analysis (math.FA)Primary 47B15 Secondary 47A55 35J25 47A10 47B35Mathematics - Functional AnalysisMathematics - Spectral Theory0103 physical sciencesFOS: MathematicsComputer Science::Symbolic Computation010307 mathematical physics0101 mathematicsSpectral Theory (math.SP)Mathematical PhysicsAnalysisMathematicsJournal of Mathematical Analysis and Applications
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