What exactly is half a derivative anyway?
William R. Green, '05
Assistant Professor
Department of Mathematics
Rose-Hulman Institute of Technology
The theory of differentiation is well-known to any student who has taken calculus. However, to make sense of a non-integer order derivative takes considerably more work. Tools are needed from complex analysis, harmonic
analysis and linear algebra to understand a half derivative. In this talk, we will begin by investigating what it means to take the square root of a matrix, and
viewing a derivative as a "really large matrix" we can begin to make sense of a
half derivative. With these simple tools, we can make sense of even crazier
objects such as derivatives of imaginary order!