Polynomials of Least Deviation from Zero in Sobolev p-Norm
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AbstractThe first part of this paper complements previous results on characterization of polynomials of least deviation from zero in Sobolev p-norm ($$1<p<\infty $$ 1 < p < ∞ ) for the case $$p=1$$ p = 1 . Some relevant examples are indicated. The second part deals with the location of zeros of polynomials of least deviation in discrete Sobolev p-norm. The asymptotic distribution of zeros is established on general conditions. Under some order restriction in the discrete part, we prove that the n-th polynomial of least deviation has at least $$n-\mathbf {d}^*$$ n - d ∗ zeros on the convex hull of the support of the measure, where $$\mathbf {d}^*$$ d ∗ denotes the number of terms in the discrete part.
2003 ◽
Vol 150
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pp. 57-70
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1999 ◽
Vol 98
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pp. 104-116
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2015 ◽
Vol 16
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pp. 167-185
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2013 ◽
Vol 24
(07)
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pp. 1350051
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1994 ◽
Vol 341
(2)
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pp. 881-894
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