Chebyshev approximation with non-continuous weight functions

Abstract

The theory of Chebyshev approximation with respect to a positive continuous (ordinary) weight function is well understood and the Remez algorithm can be used in most cases of practical interest. The problem of Chebyshev approximation with respect to a non-negative, non-continuous weight function is now under investigation by the author, who would like to hear from any reader having a problem of this type. In return for such information the author will supply the theory and methods developed to date.