Birkhoff Interpolation with Rectangular Sets of Nodes
نویسندگان
چکیده
Although it is important both in theory as well as in applications, a theory of Birkhoff interpolation with main emphasis on the shape of the set of nodes is still missing. Here we explain the problem, and then we concentrate on one of the simplest shapes (“rectangular”) in the case of bivariate uniforme Birkhoff interpolation schemes. The ultimate goal is to obtain a geometrical understanding of the solvability. We achieve this by describing several regularity criteria, illustrated by many examples. At the end we discuss several conjectures.
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