The fundamental equations for inversion of operator pencils on Banach space
| Autor: | Charles E. M. Pearce, Phil Howlett, Amie Albrecht |
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| Přispěvatelé: | Albrecht, Amie Renee, Howlett, Philip George, Pearce, C |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Essential singularity
fundamental equations singular pertubation Applied Mathematics Laurent series [2010] 47A10 47A55 47A56 Mathematical analysis Banach space resolvent Resolvent formalism Functional Analysis (math.FA) Mathematics - Functional Analysis operator pencil Bounded function FOS: Mathematics Gravitational singularity C0-semigroup Analysis Resolvent Mathematics |
| Popis: | We prove that the resolvent of a linear operator pencil is analytic on an open annulus if and only if the coefficients of the Laurent series satisfy a system of fundamental equations and are geometrically bounded. Our analysis extends earlier work on the fundamental equations to include the case where the resolvent has an isolated essential singularity. We find a closed form for the resolvent and use the fundamental equations to establish key spectral separation properties when the resolvent has only a finite number of isolated singularities. Finally we show that our results can also be applied to polynomial pencils. 18 pages: correction to published article |
| Databáze: | OpenAIRE |
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