2023/02/20 by Parvaneh Joharinad, Jürgen Jost, Joharinad, Parvaneh +5
Engineering · Mathematics · #42A05 #Advanced Numerical Analysis Techniques #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Iterative Methods for Nonlinear Equations
paper · pdf · doi:10.48550/arxiv.2302.10122
openalex publication_date 2023/02/20 · openalex created_date 2023/02/22 · openalex updated_date 2026/07/28
The more then hundred years old Bernstein inequality states that the supremum norm of the derivative of a trigonometric polynomial of fixed degree can be bounded from above by supremum norm of the polynomial itself. The reversed Bernstein inequality, that we prove in this note, says that the reverse inequality holds for functions in the orthogonal complement of the space of polynomials of fixed degree. In fact, we derived a more general result for the lower bounds on higher derivatives. These bounds are better then those obtained by applying bound for the first derivative successively several times.