Dual finite frames for vector spaces over an arbitrary field with applications

Author(s)

Dual finite frames for vector spaces over an arbitrary field with applications Patricia Mariela Morillas

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.

DOI: 10.52737/18291163-2021.13.2-1 Armenian Journal of Mathematics, 13(2) 1-36

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Keywords

Vector Spaces, Fields, Dual Frames, Hilbert Spaces, Metric Vector Spaces, Ultrametric Normed Vector Spaces

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