Szegő kernel asymptotics on some non-compact complete CR manifolds

Abstract

We establish Szegő kernel asymptotic expansions on non-compact strictly pseudoconvex complete CR manifolds with transversal CR R-action under certain natural geometric conditions. CONTENTS 1. Introduction 1 2. Preliminaries 5 2.1. The R-action on 8 2.2. The Fourier transform on 10 3. CR Bochner formula with R-action 11 3.1. CR Bochner-Kodaira-Nakano formula I 12 3.2. CR Bochner-Kodaira-Nakano formula II 15 4. Szegő kernel asymptotics 17 4.1. Complete CR manifolds 17 4.2. The operators É , É [ ½ ] , É 18 4.3. Local closed range for (0) 21 4.4. Vanishing theorems 24 4.5. Szegő kernel asymptotic expansions 26 5. Examples 34 References 35