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

Armenian Journal of Mathematics

article

Patricia Mariela Morillas¹ 

[1] Instituto de Matemática Aplicada San Luis

关键词: Vector Spaces;    Fields;    Dual Frames;    Hilbert Spaces;    Metric Vector Spaces;    Ultrametric Normed Vector Spaces;   

DOI  :  10.52737/18291163-2021.13.2-1

学科分类：环境科学（综合）

来源: National Academy of Sciences of the Republic of Armenia

【 摘 要 】

In the present paper, we study frames for finitedimensional 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.

【 授权许可】

CC BY