Comparison theorems forL-monosplines of minimal norm期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Comparison theorems forL-monosplines of minimal norm

Authors:	Georgi R. Grozev

Affiliation:	(1) Institute of Mathematics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria

Abstract:	Summary LetLM_N be the set of allL-monosplines withN free knots, prescribed by a pair (x;E) of pointsx = {x_i}₁ⁿ,a <x₁ < ... <x_n <b and an incidence matrixE = (e_ij)_i=1ⁿ,_r-1^j=0 with $left\| E right\| = sumlimits_{i = 1}^n {sumlimits_{j = 0}^{r - 1} {e_{ij} leqq N.} }$ Denote byLM_N^O the subset ofLM_N consisting of theL-monosplines withN simple knots (n=N). We prove that theL-monosplines of minimalL_p-norms inLM_N belong toLM_N^O.The results are reformulated as comparison theorems for quadrature formulae.

Keywords:	AMS(MOS): 41A15, 41A55 CR: G.1.2
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