Let be a self-adjoint extension of the Schrödinger operator with the Dirichlet boundary condition on an arbitrary open set~ of~, where and the negative part of potential belongs to the Kato class on . The purpose of this paper is to prove --estimates and gradient estimates for an operator , where is an arbitrary rapidly decreasing function on , and is defined via the spectral theorem.
Cite this article
Tsukasa Iwabuchi, Tokio Matsuyama, Koichi Taniguchi, Boundedness of spectral multipliers for Schrödinger operators on open sets. Rev. Mat. Iberoam. 34 (2018), no. 3, pp. 1277–1322DOI 10.4171/RMI/1024