Analysis of the Hodge Laplacian on the Heisenberg group

Abstract

Introduction Differential forms and the Hodge Laplacian on Hn Bargmann representations and sections of homogeneous bundles Cores, domains and self-adjoint extensions First properties of D k exact and closed forms A decomposition of L2 L kh related to the i?½ and i?½ complexes Intertwining operators and different scalar forms for D k Unitary intertwining operators and projections Decomposition of L2 L k Lp-multipliers Decomposition of Lp L k and boundedness of the Riesz transforms Applications Appendix Bibliography