Geodesic
Functional calculus generated by a square pencil
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 39, Tome 389 (2011), pp. 113-130 Cet article a éte moissonné depuis la source Math-Net.Ru

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A linear transformation $\Upsilon$ is introduced that assigns an element of a special Banach algebra to each analytic function defined on the spectrum of the pencil $\lambda\mapsto\lambda^2E+\lambda F+H$. The transformation $\Upsilon$ maps the product of two functions into the product of two elements of the algebra. As an application, a formula for a solution of the differential equation $E\ddot x(t)+F\dot x(t)+Hx(t)=f(t)$ is given. 
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     author = {I. V. Kurbatova},
     title = {Functional calculus generated by a~square pencil},
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}
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I. V. Kurbatova. Functional calculus generated by a square pencil. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 39, Tome 389 (2011), pp. 113-130. http://geodesic.mathdoc.fr/item/ZNSL_2011_389_a6/

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