Abstract
In the present paper, we delve into the study of nodal systems on the unit circle that meet certain separation properties. Our aim was to study the Hermite interpolation process on the unit circle by using these nodal arrays. The target was to develop the corresponding interpolation theory in order to make practical use of these nodal systems linked to certain mechanical models that fit these distributions.
Highlights
Hermite polynomial interpolation problems on the real line and on the bounded interval have been widely studied by many researchers
If one wants to work on the bounded interval with nodal systems that are not connected with measures, it seems convenient that the nodes have a distribution that is not far from the Chebyshev distribution
We studied the Lagrange interpolation problem on the unit circle by using nodal systems that are not connected with any measure, and they are only characterized by satisfying a separation property of the type: θ j+1 − θ j = 2π n + O( n2 )
Summary
Hermite polynomial interpolation problems on the real line and on the bounded interval have been widely studied by many researchers. Some nodal systems called well-spaced ones have been used for studying Lagrange interpolation problems They are not connected with measures, any reasonable choice of interpolation nodes fulfills the conditions of being well spaced (see [8]). If one wants to work on the bounded interval with nodal systems that are not connected with measures, it seems convenient that the nodes have a distribution that is not far from the Chebyshev distribution. This closeness can be established in terms of suitable separation properties. The advantages of using these types of nodal systems is that they can be obtained through a random uniform distribution (see the examples given in [9])
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