On spline collocation and the Hilbert transform

In this paper we examine a relationship between the spline collocation projection operator πn and the Hilbert singular integral operator H0. We use Fourier analysis to prove that under certain conditions, a commutator property holds between the two operators. More specifically, we show that for u ε...

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Bibliographic Details
Published in:Carpathian Journal of Mathematics 2015-01, Vol.31 (1), p.89-95
Main Author: Micula, Sanda
Format: Article
Language:English
Subjects:
Approximation
Commutators
Differential equations
Fourier coefficients
Fourier transformations
Mathematical integrals
Textual collocation
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Summary:In this paper we examine a relationship between the spline collocation projection operator πn and the Hilbert singular integral operator H0. We use Fourier analysis to prove that under certain conditions, a commutator property holds between the two operators. More specifically, we show that for u ε Ht, ∥(πn H0 – H0πn)u∥t ≤ Chλ∥u∥s (where h = 1/n), for some t, s and λ ε R.
ISSN:1584-2851
1843-4401
DOI:10.37193/CJM.2015.01.10