A variant of Tao's method with application to restricted sumsets

In this paper, we develop Terence Tao's harmonic analysis method and apply it to restricted sumsets. The well-known Cauchy–Davenport theorem asserts that if ∅≠A, B⊆Z/pZ with p a prime, then |A+B|⩾min{p,|A|+|B|−1}, where . In 2005, Terence Tao gave a harmonic analysis proof of the Cauchy–Davenport theorem, by applying a new form of the uncertainty principle on Fourier transform. We modify Tao's method so that it can be used to prove the following extension of the Erdős–Heilbronn conjecture: If A,B,S are non-empty subsets of Z/pZ with p a prime, then .