2 7 N ov 2 00 1 Derivatives of the L p - cosine transform
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چکیده
The L-cosine transform of an even, continuous function f ∈ Ce(S ) is defined by: H(x) = ∫ S |〈x, ξ〉|f(ξ) dξ, x ∈ R. It is shown that if p is not an even integer then all partial derivatives of even order of H(x) up to order p + 1 (including p + 1 if p is an odd integer) exist and are continuous everywhere in R\{0}. As a result of the corresponding differentiation formula, we show that if f is a positive bounded function and p > 1 then H is a support function of a convex body whose boundary has everywhere positive Gauss-Kronecker curvature.
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تاریخ انتشار 2001