Open AccessOn Finite Dimensional Hilbert Space Frames, Dual and Normalized Frames and Pseudo-inverse of the Frame Operator
Author(s) -
Loyford Njagi,
BM Nzimbi,
S.K Moindi
Publication year - 2018
Publication title -
journal of advance research in mathematics and statistics
Language(s) - English
Resource type - Journals
ISSN - 2208-2409
DOI - 10.53555/nnms.v5i11.528
Subject(s) - hilbert space , rigged hilbert space , mathematics , frame (networking) , basis (linear algebra) , hilbert r tree , hilbert manifold , generalization , mathematical analysis , dual (grammatical number) , focus (optics) , hilbert spectral analysis , space (punctuation) , inverse , operator (biology) , computer science , hilbert transform , reproducing kernel hilbert space , geometry , physics , telecommunications , art , repressor , chemistry , literature , optics , operating system , biochemistry , transcription factor , statistics , spectral density , gene
In this research paper we do an introduction to Hilbert space frames. We also discuss various frames in the Hilbert space. A frame is a generalization of a basis. It is useful, for example, in signal processing. It also allows us to expand Hilbert space vectors in terms of a set of other vectors that satisfy a certain condition. This condition guarantees that any vector in the Hilbert space can be reconstructed in a numerically stable way from its frame coe?cients. Our focus will be on frames in ?nite dimensional spaces.