Abstract
Conditions for a system of contractions and translations of a function to be a Riesz basis are given.
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REFERENCES
V. I. Filippov and P. Oswald, “Representation in Lp by series of translates and dilates of one function,” J. Approx. Theory, 82 (1995), no. 1, 15-29.
T. N. Saburova, “On bases in C[0, 1] of Faber-Schauder type,” in: The Theory of Functions and Approximations. Pt. 3 [in Russian], Proceedings of the 3d Saratov Winter Workshop (Saratov, 1986), Saratov, 1988, pp. 44-46.
P. Halmos, A Hilbert Space Problem Book, London, 1967.
B. Sz.-Nagy and C. Foia?, Analyse harmonique des opérateurs de l'espace de Hilbert, Bucharest, 1967.
F. Riesz and B. Sz.-Nagy, Leçons d'analyse fonctionnelle, Gauthier-Villars, Paris, and Akademiai Kiado, Budapest, 1965.
Functional Analysis (S. G. Krein, editor) [in Russian], “Reference Mathematical Library” Series, Nauka, Moscow, 1972
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Terekhin, P.A. Riesz Bases Generated by Contractions and Translations of a Function on an Interval. Mathematical Notes 72, 505–518 (2002). https://doi.org/10.1023/A:1020536412809
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DOI: https://doi.org/10.1023/A:1020536412809