V. I. Kolyada

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We study the uniformly bounded orthonormal systemU of functions u ( ) n (x)= ( ) n (cos x)(sin x) , x ∈ [0, ], where { ( ) n }∞n=0 ( > 0) is the normalized system of ultraspherical polynomials.We investigate some approximation properties of the systemU and we show that these properties are similar to one’s of the trigonometric system. First, we obtain(More)
The study of the normability of the Lorentz spaces L(R, μ) goes back to the work of G.G. Lorentz [10, 11] (see also [13, 3, 2] for a more recent account of the normability results for the weighted Lorentz spaces). The condition defining these spaces is given in terms of the distribution function and, equivalently, the non-increasing rearrangement of f (see(More)
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