A note on the heat kernel on the Heisenberg group

Abstract

We describe the analytic continuation of the heat kernel on the Heisenberg group ℍ n (ℝ). As a consequence, we show that the convolution kernel corresponding to the Schrödinger operater e isL is a smooth function on ℍ n (ℝ) \ S s , where S s = {(0, 0, ± sk ) ∈ ℍ n (ℝ) : k = n , n + 2, n + 4,…}. At every point of S s the convolution kernel of e isL has a singularity of Calderón–Zygmund type.

Locations

• Bulletin of the Australian Mathematical Society - View - PDF