A regulator for curves via the Heisenberg group

Braid Group Actions via Categorified Heisenberg Complexes

We construct categorical braid group actions from 2-representations of a Heisenberg algebra. These actions are induced by certain complexes which generalize spherical (Seidel-Thomas) twists and are reminiscent of the Rickard complexes defined by Chuang-Rouquier. Conjecturally, one can relate our complexes to Rickard complexes using categorical vertex operators.

A Necessary Condition for Weyl-Heisenberg Frames

p-ESTIMATES FOR SINGULAR INTEGRALS AND MAXIMAL OPERATORS ASSOCIATED WITH FLAT CURVES ON THE HEISENBERG GROUP

The maximal function along a curve (t, γ (t), tγ (t)) on the Heisenberg group is discussed. The L p-boundedness of this operator is shown under the doubling condition of γ ′ for convex γ in R. This condition also applies to the singular integrals when γ is extended as an even or odd function. The proof is based on angular LittlewoodPaley decompositions in the Heisenberg group.

Sampling theorems for the Heisenberg group

In the first part of the paper a general notion of sampling expansions for locally compact groups is introduced, and its close relationship to the discretisation problem for generalised wavelet transforms is established. In the second part, attention is focussed on the simply connected nilpotent Heisenberg group H. We derive criteria for the existence of discretisations and sampling expansions ...

S Theorem for the Heisenberg Group

If an integrable function f on the Heisenberg group is supported on the set B × R where B ⊂ Cn is compact and the group Fourier transform f̂(λ) is a finite rank operator for all λ ∈ R \ {0}, then f ≡ 0.