TY - JOUR
AU - Morillas, Patricia Mariela
PY - 2021/05/15
Y2 - 2021/06/16
TI - Dual finite frames for vector spaces over an arbitrary field with applications
JF - Armenian Journal of Mathematics
JA - Armen.J.Math.
VL - 13
IS - 2
SE - Articles
DO - 10.52737/18291163-2021.13.2-1
UR - http://armjmath.sci.am/index.php/ajm/article/view/479
SP - 1-36
AB - <p>In the present paper, we study frames for finite-dimensional vector spaces over an arbitrary field. We develop a theory of dual frames in order to obtain and study the different representations of the elements of the vector space provided by a frame. We relate the introduced theory with the classical one of dual frames for Hilbert spaces and apply it to study dual frames for three types of vector spaces: for vector spaces over conjugate closed subfields of the complex numbers (in particular, for cyclotomic fields), for metric vector spaces, and for ultrametric normed vector spaces over complete non-archimedean valued fields. Finally, we consider the matrix representation of operators using dual frames and its application to the solution of operators equations in a Petrov-Galerkin scheme.</p>
ER -