Abstract
Systems of integer translates arise in the context of approximation theory, wavelet analysis, and in the theory of shift invariant spaces. After a review of the known properties for integer translates of one square summable function, we explore various levels of linear independence of integer translates of a finite number of functions in terms of properties of the associated Gramian matrix. In some cases, the results are not a straightforward generalization of the case when a single function is considered.
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Saliani, S. (2015). On Various Levels of Linear Independence for Integer Translates of a Finite Number of Functions. In: Balan, R., Begué, M., Benedetto, J., Czaja, W., Okoudjou, K. (eds) Excursions in Harmonic Analysis, Volume 3. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-13230-3_9
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DOI: https://doi.org/10.1007/978-3-319-13230-3_9
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