Functional calculus generated by a square pencil

A linear transformation Υ which assigns to each analytic function defined on the spectrum of the pencil λ {mapping} λ 2E + λF + H an element of a special Banach algebra is defined. The transformation Υ maps the product of two functions to the product of two elements of the algebra. As an application, as fornula for the solution of the differential equation Eẍ(t)+Fẋ(t)+Hx(t)=f(t) is given. Bibliography: 12 titles. © 2012 Springer Science+Business Media, Inc.