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. RAN. Ser. Mat., 2001, Volume 65, Issue 2,Pages 187

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Function systems obtained using translates and dilates of a single function in the paces $E_\varphi$ with $\lim_{t\to\infty}\frac{\varphi(t)}t=0$

V. I. Filippov

Saratov State University named after N. G. Chernyshevsky

Abstract: We solve Ul'yanov's problem [1] of representing elements of class $\varphi(L)$ as series with respect to arbitrary function systems.

MSC: 41A30, 41A65, 42C10, 42C15, 46B15, 46T30

Received: 13.05.1999

DOI: 10.4213/im331