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The generalized inverses of differentiation and integration
Expositiones Mathematicae ( IF 0.8 ) Pub Date : 2021-07-24 , DOI: 10.1016/j.exmath.2021.07.004
Steven H. Weintraub 1
Affiliation  

Let Pn be the vector space of polynomials of degree at most n, equipped with the inner product f,g=11f(x)g(x)dx. Let D:PnPn1 be the differentiation operator and I:Pn1Pn be the integration operator. In this paper the generalized (Moore–Penrose) inverses of D and I are computed. The answer for D is straightforward, though perhaps somewhat unexpected. The answer for I requires more work, and involves Legendre polynomials in an unexpected way.



中文翻译:

微分和积分的广义逆

n 最多为次数多项式的向量空间 n, 配备内积 F,G=-11F(X)G(X)dX. 让Dnn-1 是微分算子和 一世n-1n成为整合运营商。在本文中,广义(Moore-Penrose)逆D一世被计算。答案为D很简单,虽然可能有点出乎意料。答案为一世 需要更多的工作,并以意想不到的方式涉及勒让德多项式。

更新日期:2021-07-24
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