%0 Journal Article
%T SOME OPERATORS ACTING ON WEIGHTED SEQUENCE SPACES AND APPLICATIONS
%J Scientia Iranica
%I Sharif University of Technology
%Z 1026-3098
%A LIZAMA, CARLOS
%D 2013
%\ 12/01/2013
%V 20
%N 6
%P 1765-1772
%! SOME OPERATORS ACTING ON WEIGHTED SEQUENCE SPACES AND APPLICATIONS
%K Weighted sequence spaces
%K Chebyshev polynomials
%K non autonomous Cauchy problem
%K Operator theory
%K Bloch equation
%K Magnetic resonance imaging
%R
%X 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.
%U http://scientiairanica.sharif.edu/article_3418_7813bde404e86370d150b9de6bbe5e64.pdf