平面上的$C^{m}$半代数截面

Pub Date : 2021-01-16 DOI:10.2969/jmsj/86258625

C. Fefferman, Garving K. Luli

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引用次数: 6

摘要

对于R上的多项式P1，···，Pr，Q1，··，Qs。（我们允许r＝0或s＝0的情况。）半代数函数φ：E→ R是一个函数，其图{（x，φ（x））:x∈E}是半代数集。我们用C和C位置来定义光滑度。这里，Cm（R，R）表示R上所有R值函数的空间，其直到m阶的导数是连续的并且在R上有界。Cloc

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$C^{m}$ semialgebraic sections over the plane

for polynomials P1, · · · , Pr, Q1, · · · , Qs on R . (We allow the cases r = 0 or s = 0.) A semialgebraic function φ : E → R is a function whose graph {(x, φ(x)) : x ∈ E} is a semialgebraic set. We define smoothness in terms of C and C loc. Here, C m ( R,R ) denotes the space of all R-valued functions on R whose derivatives up to order m are continuous and bounded on R. C loc ( R,R ) denotes the space of R-valued functions on R with continuous derivatives up to order m. If D = 1, we write C (R) and C loc (R ) in place of C ( R,R )

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