International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 20, Pages 3237-3245
doi:10.1155/IJMMS.2005.3237

Wavelet-type frames and wavelet-type bases

Abstract

The concepts of basis and frame are studied in the classical literature of functional analysis, Fourier analysis, and wavelet theory in a wide range. In this paper, we consider an operator-theoretic approach to discrete frame theory on a separable Hilbert space. For this purpose, we define a special type of frames and bases, called wavelet-type frames and wavelet-type bases, obtained by acting with a family of bounded linear operators on some vectors, and then investigate the elementary properties of these concepts.