Functional calculus generated by a square pencil
type: Item
instance of: scholarly article
title: Functional calculus generated by a square pencil
zbMATH Open document ID: 1269.47015
author: I. V. Kurbatova
published in: Journal of Mathematical Sciences (New York)
publication date: 2012-11-28T00:00:00Z
review text: Let \(E,F,H\) be bounded linear operators acting from a Banach space \(X\) to a Banach space \(Y\). The function \(\lambda\rightarrow \lambda^2E+\lambda F+\lambda H\) is called a square pencil. The spectrum of a square pencil is the set \(\sigma( E, F, H)\) of all complex \(\lambda\) for which the operator \(\lambda^2E+\lambda F+\lambda H\) has no inverse. The author constructs a functional calculus \(\Upsilon\) from the space of functions which are analytic on the spectrum of a quadratic pencil, into the Banach algebra \(B_{(E,F,H)}(X,Y)\). By applying the functional calculus, a solution for the differential equation \( E \ddot x(t) + F\dot x(t) + Hx(t) = f(t) \) is obtained.
reviewed by: M. B. Ghaemi
Mathematics Subject Classification ID: 47A60
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 46H05
Mathematics Subject Classification ID: 47A56
zbMATH DE Number: 6110766
describes a project that uses: RODAS
MaRDI profile type: Publication
full work available at URL: s10958-012-0769-4
OpenAlex ID: W2092490501
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cites work: Banach algebras associated with linear operator pencils
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DOI: 10.1007/S10958-012-0769-4
description: scientific article; zbMATH DE number 6110766