Amit Ophir

Hebrew University of Jerusalem | HUJI · Einstein Institute of Mathematics

Motivated by questions about $\mathbb{C}_p$-valued Fourier transform on the locally compact group $(\mathbb{Q}_p^d,+)$, we study invariant norms on the $p$-adic Schr\"odinger representation of the Heisenberg group. Our main result is a minimality and rigidity property for norms in a family of invariant norms parameterized by a Grassmannian. This fa...

Let F be a finite extension of Q_p. We show that every Schwartz function on F, with values in an algebraic closure of Q_p, is the uniform limit of a sequence of Schwartz functions, whose Fourier transforms tend uniformly to 0. The proof uses the notion of q-binomial coefficients and some classical identities between them.

Let (X,d)(X,d) be any finite metric space with nn elements. We show that there are two pairs of distinct elements in XX that determine two nearly equal distances in the sense that their ratio differs from 1 by at most 9lognn2. This bound (apart for the multiplicative constant) is best possible and we construct a metric space that attains this bound...