Almost normed spaces of functions with polynomial asymptotic behaviour

Kudryavtsev, L. D.

doi:10.1070/sm2003v194n01abeh000708

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The Factorizational Approach1

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2006

2007

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Cited by 2 publications

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“…The case i = 0 in Theorem 3.1 is due to Kudryavtsev: a sketch of the proof is given in [17], a complete proof appears in [19], and a simplified but still lenghty proof is in [21]. Our proposed proof of Theorem 3.1 in §6 is very simple, but we do not give the explicit expressions of the coefficients of the polynomial P in terms of f (n+1) which play a vital role in Kudryavtsev's studies.…”

Section: The Factorizational Approachmentioning

confidence: 99%

Polynomial asymptotic expansions in the real domain: the geometric, the factorizational, and the stabilization approaches

Granata

2007

Anal Math

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A b s t r a c t . The problem of the existence of an asymptotic expansion of type f (x) = anx n + an−1x n−1 + · · · + aix i + o(x i ), x → +∞, is thoroughly studied, comparing and completing the known results obtained through the three different approaches mentioned in the title. A unifying thread is provided by the canonical factorizations of the differential operator D n . Particularly meaningful are several characterizations of the polynomial asymptotic expansions of an nth order convex function.

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Section: The Factorizational Approachmentioning

confidence: 99%