Inversion of operator pencils on Banach space using Jordan chains when the generalized resolvent has an isolated essential singularity

24 Feb 2020 Albrecht Amie Howlett Phil Verma Geetika

We assume that the generalized resolvent for a bounded linear operator pencil mapping one Banach space onto another has an isolated essential singularity at the origin and is analytic on some annular region of the complex plane centred at the origin. In such cases the resolvent operator can be represented on the annulus by a convergent Laurent series and the spectral set has two components---a bounded component inside the inner boundary of the annulus and an unbounded component outside the outer boundary... (read more)

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