Let f be a complex valued function on the finite Abelian group A=(Z_N)^d with Fourier transform F.

A variant of the uncertainty principle (known as annihilating pairs) states that for any subsets E, S of A, we have that the ell-2-norms of f and F satisfy the inequality:

        ||f|| <= C || f_E ||+||F_S||

for some constant C dependent only on E and S (Ghobber 2011). Here f_E, F_S are the restrictions of f and F to the complements of E and S respectively (zero elsewhere). 

Recently, this result was extended by Iosevich, Jaming, and Mayeli under the non-trivial assumption of the existence of a Fourier restriction estimate.
    
In this paper, we explore the extension of these results from classical L^p spaces to Orlicz spaces over A. Using generalized restriction estimates between complimentary Young functions, we investigate the extent to which these inequalities hold in these broader functional spaces. The main contribution is the derivation of inequalities for annihilating pairs in Orlicz spaces under these restriction assumptions.

Talk can be livestreamed on zoom meeting ID 986 2892 7517 - send request to jonathan.pakianathan@rochester.edu at least 2 days before talk to guarantee this option. Video of the lecture will be made available after the talk also (not live).