Finite field analogue of restriction theorem for general measures


Changhao Chen


University of New South Wales


Tue, 24/04/2018 - 12:00pm to 1:00pm


RC-4082, The Red Centre, UNSW


We study Fourier transformation of functions in vector spaces over finite fields. Specially we talk about finite field analogue of restriction problem, a basic problem in harmonic analysis. G. Mockenhaupt and T. Tao initially studied the finite field analogue of restriction problem. By adapting their arguments we obtain finite field analogue of Mockenhaupt-Mitsis-Bak-Seenger restriction theorem. Furthermore, inspired by the constructions of K. Hambrook, I. Laba, X. Chen for the Euclidean setting, we show that the range of the exponentials is sharp for the finite fields setting.

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