UM Math Graduate Student Seminar

Hao Kang
University of Miami

will present

On Some Classical Analysis Problems by Baire Category Theorems

Friday, February 10, 2017, 5:00pm
Ungar Building Room 402


Abstract:

In this talk, I will review Baire Category Theorem (BCT) and see some classical analysis problems in the view of functional analysis, including:
1. Is there a function of C[0,1] continuous at rational points but discontinuous at irrational points?
2. How "many" functions continuous everywhere but differentiable nowhere?
3. Do the Fourier series of every continuous periodic function converge to itself point-wise?

Some derived theorems from BCT such as uniform boundedness theorem and open mapping theorem and in particular their applications are also introduced.

 


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