Abstract: P.L.Chebyshev's pupil E.I. Zolotarev has found the best uniform rational approximation of a signum function on two real intervals. Known today as Zolotarev fractions, these approximations have many interesting properties, which, in particular, led to their application in electrical engineering.
Many properties of Chebyshev polynomials, such as the solution of many extreme problems in the geometric theory of functions, behavior of composition, and characterization through extreme values, have their analogues for Zolotarev fractions. We will also discuss the higher analogues of Zolotarev's fractions that arise in the optimal synthesis of multiband electric filters.
Bio: Andrei Bogatyrev, Professor of Moscow State University and HSE University, Professor of Russian Academy of Sciences; S.V.Kovalevskaya Prize of RAS (2009).
Field of Research: Complex and numerical analysis, algebraic curves and moduli, math physics.
