| Language |
English
|
| From |
2009/07/10 14:00
|
| To |
2009/07/10 17:00
|
| Place | Room 609, Building No.6, Faculty of Science, Kyoto University |
| Seminar Name | Kyoto Dynamical Systems Seminar |
| Title |
Maximum and Minimum values of some continuous nowhere differentiable functions |
| Field |
Geometry
Analysis
|
| Speakers | Pieter Allaart, Kiko Kawamura |
| Affiliation | University of North Texas |
| Abstract | 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.
|
| Link | http://www.math.kyoto-u.ac.jp/dynamics/ |
|