A. P. Goncharov

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We show that the polynomial wavelets suggested by T.Kilgor and J.Prestin in [12] form a topological basis in the space C∞[−1, 1]. During the last twenty years wavelets have found a lot of applications in mathematics, physics and engineering. Our interest in wavelets is related to their ability to represent a function, not only in the corresponding Hilbert(More)
‖f ‖ ≤ Crq ‖f‖ 1−q/r ‖f ‖ was proved by Kolmogorov in [11] for f ∈W r ∞(R). Here ‖ · ‖ means ‖ · ‖L∞(R) and the sharp constant Crq = Kr−qK −1+q/r r is given in terms of the Favard constants Kp := 4 π ∑∞ n=0 [ (−1) 2n+1 p+1 . For the definition of the Sobolev space W r ∞(R) see e.g. [4, Ch. 1.5]. The first results of this type (the case q = 1, r = 2) were(More)