Paul Gartside: Hilbert's 13th Problem
Prof. dr. Paul Gartside
University of Pittsburgh, ZDA
14. maj 2009
The 13th Problem from Hilbert's famous list asks: can every continuous function of three variables be written as a composition of functions of two variables? Hilbert expected the answer to be ‘no'.
In 1954 Vitushkin proved that there are continuously differentiable functions of 3 variables which can not be written as a composition of continuously differentiable functions of 2 variables. Thereby giving the kind of negative result Hilbert was expecting.
But three years later Kolmogorov gave a remarkable positive solution - in fact every continuous function of n variables can be written as a composition of functions of just one variable plus addition.
In this talk the speaker will outline a proof of Kolmogorov's theorem and of Vitushkin's result, and then discuss ongoing work of the speaker and Feng Ziqin surrounding Hilbert's 13th Problem.
