Sharif University of TechnologyScientia Iranica1026-309820620131201SOME OPERATORS ACTING ON WEIGHTED SEQUENCE SPACES AND APPLICATIONSSOME OPERATORS ACTING ON WEIGHTED SEQUENCE SPACES AND APPLICATIONS176517723418ENCARLOSLIZAMADepartamento de Matematica y Ciencia de la Computacion, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307-Correo2, Santiago, ChileJournal Article20131021This 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.http://scientiairanica.sharif.edu/article_3418_7813bde404e86370d150b9de6bbe5e64.pdf