SOME OPERATORS ACTING ON WEIGHTED SEQUENCE SPACES AND APPLICATIONS

This paper considers the problem of constructing an evolution family for the linear non autonomous Cauchy problem u(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 is sought in the form of a series of Chebyshev polynomials. Then, by de ning appropriate weighted sequence spaces and matrices of linear operators, we are able to obtain a suf- cient condition - based only in the given data - for the representation of the solution of the initial value problem (). The method is motivated for practical considerations in the context of Magnetic Resonance Imaging.