セミナー

発表言語 英語
開催日 2009年07月10日 14時00分
終了日 2009年07月10日 17時00分
開催場所京都大学理学部6号館609号室
セミナー名京都力学系セミナー
タイトル Maximum and Minimum values of some continuous nowhere differentiable functions 
分野 幾何
解析
講演者名Pieter Allaart, Kiko Kawamura
講演者所属University of North Texas
概要 The goal of our research is to find new techniques to analyze
fractal functions since several powerful methods of classical
calculus are clearly unsuited to them. For instance, a basic
application of a derivative is finding extreme values of
a differentiable function. However, if a function is nowhere
differentiable, how can we find the extreme values?

We consider the functions T_n (x) defined as the n-th partial
derivative of Lebesgue's singular function L_a (x) with respect
to a, and show that T_n is continuous but nowhere differentiable
for each n.

In the first half of the talk, Kawamura explains the problem
of finding maximum and minimum points of T_1, T_2 and T_3.
Some interesting unsolved problems and conjectures will be
discussed by Allaart in the last half of the talk.
リンクhttps://www.math.kyoto-u.ac.jp/dynamics/