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Wavelet-type frames and wavelet-type bases

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  • M. M. Shamooshaky

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.

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  • M. M. Shamooshaky, 2005. "Wavelet-type frames and wavelet-type bases," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-9, January.
    • Handle: RePEc:hin:jijmms:149630
    DOI: 10.1155/IJMMS.2005.3237
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