Some operators acting on weighted sequence spaces and applications

This paper considers the problem of constructing an evolution family for thelinear nonautonomous cauchy problem:() @@tu(t) ?? a(t)u(t) = 0; u(??1) = x 2 rn;where a 2 c([??1; 1], rnn). the essence of the method is that the evolution family issought in the form of a series of chebyshev polynomials. then, by dening appropriateweighted sequence spaces and matrices of linear operators, we are able to obtain a sucientcondition - based only in the given data - for the representation of the solution of the initialvalue problem (*). the method is motivated for practical considerations in the context ofmagnetic resonance imaging.