Geodesic
Representation systems obtained using translates and dilates of a~single function in multidimensional spaces $E_{\varphi}$
Izvestiya. Mathematics , Tome 76 (2012) no. 6, pp. 1257-1270.

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We consider function systems obtained using translates and dilates of a single function in multidimensional spaces $E_{\varphi}$.
Keywords: generalized Orlicz classes, generalized Orlicz spaces, representation systems, approximation in spaces $E_{\varphi}$, function systems of translates and dilates of a single function. 
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V. I. Filippov. Representation systems obtained using translates and dilates of a~single function in multidimensional spaces $E_{\varphi}$. Izvestiya. Mathematics , Tome 76 (2012) no. 6, pp. 1257-1270. http://geodesic.mathdoc.fr/item/IM2_2012_76_6_a9/

[1] V. I. Filippov, “Function systems obtained using translates and dilates of a single function in the paces $E_\varphi$ with $\lim_{t\to\infty}\frac{\varphi(t)}t=0$”, Izv. Math., 65:2 (2001), 389–402 | DOI | MR | Zbl

[2] P. L. Ul'yanov, “Representation of functions by series and classes $\varphi(L)$”, Russian Math. Surveys, 27:2 (1972), 1–54 | DOI | MR | Zbl

[3] P. L. Ul'yanov, “Remarks on mean convergence”, Math. Notes, 21:6 (1977), 455–461 | DOI | MR | Zbl | Zbl

[4] V. I. Filippov, P. Oswald, “Representation in $L^p$ by series of translates and dilates of one function”, J. Approx. Theory, 82:1 (1995), 15–29 | DOI | MR | Zbl

[5] V. I. Filippov, “On the completeness and other properties of some function systems in $L_p$, $0

\infty$”, J. Approx. Theory, 94:1 (1998), 42–53 | DOI | MR | Zbl

[6] V. I. Filippov, “On subsystems of the Faber–Schauder system in functional spaces”, Soviet Math. (Iz. VUZ), 35:2 (1991), 90–97 | MR | Zbl

[7] R. E. Zink, “On a theorem of Goffman concerning Schauder series”, Proc. Amer. Math. Soc., 21:3 (1969), 523–529 | DOI | MR | Zbl

[8] V. G. Krotov, “Representation of measurable functions by series in the Faber–Schauder system, and universal series”, Math. USSR-Izv., 11:1 (1977), 205–218 | DOI | MR | Zbl | Zbl

[9] V. I. Filippov, “Linear continuous functionals and representation of functions by series in the spaces $E_{\varphi}$”, Anal. Math., 27:4 (2001), 239–260 | DOI | MR | Zbl

[10] J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Math., 1034, Springer-Verlag, Berlin, 1983 | DOI | MR | Zbl

[11] K. Yosida, Functional analysis, Grundlehren Math. Wiss., 123, Springer-Verlag, Berlin–Göttingen–Heidelberg; Academic Press, New York, 1965 | MR | MR | Zbl | Zbl

[12] A. A. Talaljan, “On approximation properties of certain incomplete systems”, Math. USSR-Sb., 43:4 (1982), 443–471 | DOI | MR | Zbl | Zbl