中国科学院数学与系统科学研究院

数学研究所

学术报告

集合论讨论班

报告人：Maxim Burke (University of Prince Edward Island)

题  目：Comonotone approximation and interpolation by entire functions

时  间：2024.10.09（星期三）10：30-12：00

地  点：思源楼S813

摘  要：We discuss some theorems on approximation of a real function f whose derivatives up to order n are piecewise monotone by an entire function g whose derivatives up to order n are comonotone with those of f (increasing and decreasing on the same intervals) with interpolation on a closed discrete set. The work has its origins in the problem of finding entire order-isomorphisms of everywhere nonmeager subsets of R of cardinality aleph_1. One of the theorems depends on a conjecture regarding the nature of the set of (n+1)-tuples (f(1),f'(1),f''(1),...)  of final values of C^n functions f on [0,1] whose derivatives at the origin are zero and whose nth derivative is increasing but not constant.