SOME OPERATORS ACTING ON WEIGHTED SEQUENCE SPACES AND APPLICATIONS

LIZAMA, CARLOS

SOME OPERATORS ACTING ON WEIGHTED SEQUENCE SPACES AND APPLICATIONS

Author

CARLOS LIZAMA

Departamento de Matematica y Ciencia de la Computacion, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307-Correo2, Santiago, Chile

Abstract

This paper considers the problem of constructing an evolution family for

the linear non autonomous Cauchy problem

()

@

@t

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.

Keywords

Weighted sequence spaces

Chebyshev polynomials

non autonomous Cauchy problem

Operator theory

Bloch equation

Magnetic resonance imaging