Decay and Strichartz estimates for Klein–Gordon equation on a cone I: Spinless case

Abstract

Abstract We consider the solutions of the Klein–Gordon equation in the 2 + 1 2{+}1 -dimensional space-time which gravity is analyzed, i.e., the manifold ℝ t × ℝ + × ℝ / 2 ⁢ π ⁢ α ⁢ ℤ {\mathbb{R}_{t}\times\mathbb{R}_{+}\times\mathbb{R}/2\pi\alpha\mathbb{Z}} created by a massive point particle. Using the Schwartz kernel of resolvent and spectral measure for Schrödinger operator on the spinless cone, we prove the dispersive estimates and Strichartz estimates for the Klein–Gordon equation. In a future paper, we will consider the problem on the spinning cone.