Colloquium at Math Department at WVU, Spring 2020
Date: Wednesday, April 22, 4-4:50pm. Preceded with refreshments, 3:30-4:00pm, in the math faculty lounge.
Location: 315 Armstrong Hall
Speaker: Professor Adrian Tudorascu, Department of Mathematics, West Virginia University
Title: What to do when we cannot differentiate under the integral sign
Abstract:
Differentiating functions f=f(x) defined as integrals of g(x,y)dy can sometimes be tricky, and must be avoided when we cannot prove that the partial derivative of g with respect to x is Lebesgue integrable. I plan to present an elementary solution to a Fourier transform-type problem; uniform continuity is obtained by a straight forward argument but Lipschitz continuity is fairly delicate, yet doable without resorting to explicitly computing the transform (which is sometimes impossible, anyway). Graduate students are especially encouraged to attend as this type of problem has showed up on the Analysis PhD Entrance Exam.