By Klin M., et al.
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Extra info for Algebraic combinatorics in mathematical chemistry
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Our next theorems show that the normalized moments of admissible kernels satisfy the Turán inequalities. 34 | George Csordas Theorem 23 (G. Csordas and R. S. Varga ). Let ???? : ℝ ????→ ℝ be an admissible ker nel. Let ∞ ∞ ???? ????(????) := ∫ ????(????) cos(????????) ???????? = ∑ ???? (−????2 )???? , (8) (2????)! ????=0 0 where the moments are defined by ∞ ???????? := ∫ ????2???? ????(????) ???????? (???? ≥ 0). 0 If log(????(√????)) is concave on (0, ∞), then the Turán inequalities hold ( for ???? ≥ 1), ????????2 − ????????−1 ????????+1 ≥ 0, where ???????? := ????!
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Algebraic combinatorics in mathematical chemistry by Klin M., et al.