Shamooshaky, M. M. Wavelet-type frames and wavelet-type bases. (English) Zbl 1085.42021 Int. J. Math. Math. Sci. 2005, No. 20, 3237-3245 (2005). Summary: 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. MSC: 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems Keywords:wavelet-type normalized tight frames; Riesz basis; orthonormal basis; Hilbert space PDFBibTeX XMLCite \textit{M. M. Shamooshaky}, Int. J. Math. Math. Sci. 2005, No. 20, 3237--3245 (2005; Zbl 1085.42021) Full Text: DOI EuDML