Chebyshev ansatz for multiband approximation: an overview

Optimization problem for an electrical filter is a multiband generalization of the third Zolotarev problem about the best uniform approximation of the Sign function. The problem attracted attention of many prominent mathematicians. One of the approaches to the practical solution of the problem is to use an analytic formula (Ansatz) with few unknown parameters. A survey of the recent developments in the topic will be given.