Pilipović, S., Stoeva, D. T. (2011): Analysis of conditions for frame functions, examples with the orthogonal functions., in: Integral Transforms Spec. Funct. 22, 311-318. (article)

Abstract:

In order to perform the analysis and the synthesis of a signal, one has to use series decompositions via appropriately chosen functions as a frame. Usually, the analysis and synthesis in the time-frequency analysis are realized through discrete integral transforms based on the series expansions via over-determined sequences of special functions.\par The authors analyse the property of free functions as a Banach frame for a Banach space, respectively Fréchet frame for a Fréchet space. Examples with the orthogonal functions in Hilbert spaces describes the assertions.

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