Surprising applications and possible extensions of Dellsarte's method

Paper presented at Strathmore International Math Research Conference on July 23 - 27, 2012This is a short informal survey on some surprising applications of Delsarte's method, written for anyone being interested. I try to keep it as short and as informative as possibleThis is a short informal survey on some surprising applications of Delsarte's method, written for anyone being interested. I try to keep it as short and as informative as possibl

A superadditivity and submultiplicativity property for cardinalities of sumsets

For finite sets of integers A1, . . . ,An we study the cardinality of the n-fold sumset A1 + · · · + An compared to those of (n − 1)-fold sumsets A1 + · · · + Ai−1 + Ai+1 + · · · + An. We prove a superadditivity and a submultiplicativity property for these quantities. We also examine the case when the addition of elements is restricted to an addition graph between the sets

A fourier analytic approach to the problem of mutually unbiased bases

We give a new approach to the problem of mutually unbiased bases (MUBs), based on a Fourier analytic technique borrowed from additive combinatorics. The method provides a short and elegant generalization of the fact that there are at most d + 1 MUBs in d. It may also yield a proof that no complete system of MUBs exists in some composite dimensions - a long standing open problem