The fundamental blossoming inequality in Chebyshev spaces. I: Applications to Schur functions
The classical Chebyshev theorem says how to obtain the minimum and maximum values of a symmetric multiaffine function of \(n\) variables with a prescribed sum. It is shown that, given two functions in an extended Chebyshev space good for design, a similar result can be stated for the minimum and maximum values of the blossom of the first function with a prescribed value for the blossom of the second one. Moreover, a simple geometric condition on the control polygon of the planar parametric curve defined by the pair of functions ensuring the uniqueness of the solution to the corresponding optimization problem is given. This provides a fundamental blossoming inequality associated with each extended Chebyshev space good for design. This inequality proves to be a tool to derive some new inequalities involving Schur functions which generalize the classical MacLaurin's and Newton's inequalities.
scientific article; zbMATH DE number 6849390
scientific article