## frame

Njagi L, Nzimbi BM, Moindi SK. "

ON FINITE DIMENSIONAL HILBERT SPACE FRAMES, DUAL AND NORMALIZED FRAMES AND PSEUDO-INVERSE OF THE FRAME OPERATOR."

*Journal of Advance Research in Mathematics And Statistics (ISSN: 2208-2409)*. 2018;5(11):11-14.

AbstractIn 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.

Njagi L, Nzimbi BM, Moindi SK. "

ON ANALYSIS AND SYNTHESIS OPERATORS AND CHARACTERIZATION OF SYNTHESIS MATRIX OF A FRAME IN TERMS OF FRAME OPERATOR."

*Journal of Advance Research in Mathematics And Statistics (ISSN: 2208-2409)*. 2018;5(12):01-10.

AbstractIn this research paper we introduce the operators associated with a frame. That is the Analysis and the Synthesis Operators and their basic properties. The structure of matrix representation of the Synthesis operator is also analysed. This matrix is what most frame constructions in fact focus on. The frame operator which is just the joining together of the analysis and synthesis operators is fundamental for the reconstruction of signals form frame coefficients. We also give a complete characterization of the synthesis matrix in terms of the frame operator.