A Theory of Extended Pseudo-Biorthogonal Bases

Hidemitsu OGAWA, Nasr-Eddine BERRACHED

Summary :

This paper introduces the concept of an extended pseudo-biorthogonal basis" (EPBOB), which is a generalization of the concepts of an orthonormal (OB), a biorthonormal (BOB), a pseudo-orthogonal (POB), and a pseudo-biorthogonal (PBOB) bases. Let H_N be a subspace of a Hilbert space H. The concept of EPBOB says that we can always construct a set of 2M (MN) elements of H but not necessarily all in H_N such that like BOB any element f in H_N can be expressed by f^MΣ_m=1(f,φ^*_m)φ_m. For a better understanding and a wide application of EPBOB, this paper provides their characterization and shows how they preserve the formalism of BOB. It also shows how to construct them.

• Publication: IEICE TRANSACTIONS on Information Vol.E76-D No.8 pp.890-897
• Publication Date: 1993/08/25
• Type of Manuscript: PAPER
• Category: Image Processing, Computer Graphics and Pattern Recognition

Authors

Hidemitsu OGAWA
Nasr-Eddine BERRACHED

Keyword

extended pseudo-biorthogonal basis,  EPBOB,  biorthonormal basis,  pseudo-orthogonal basis,  pseudo-biorthogonal basis