Estimates of Lebesgue constants for Lagrange interpolation processes by rational functions under mild restrictions to their fixed poles

We estimate the Lebesgue constants for Lagrange interpolation processes on one or several intervals by rational functions with fixed poles. We admit that the poles have accumulation points on the intervals. To prove it we use an analogue of the inverse polynomial image method for rational functions with fixed poles.
The talk is based on a joint work with Sergei Kalmykov.