| 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/ |
|