On spline collocation and the Hilbert transform


Micula, Sanda


Abstract

carpathian_2015_31_1_089_095_abstract

In this paper we examine a relationship between the spline collocation projection operator \pi_n and the Hilbert singular
integral operator {\mathcal{H}_0}. 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 \in H^t, ||(\pi_n {\mathcal{H}_0} - {\mathcal{H}_0} \pi_n)u||_t \le C h^{\la} ||u||_s (where h=1/n), for some t, s and \la \in \R.

Additional Information

Author(s)

Micula, Sandra