Boundedness of spectral multipliers for Schrödinger operators on open sets
type: Item
instance of: scholarly article
title: Boundedness of spectral multipliers for Schrödinger operators on open sets
DOI: 10.4171/RMI/1024
author: Tsukasa Iwabuchi
author: Tokio Matsuyama
author: Koichi Taniguchi
published in: Revista Matemática Iberoamericana
publication date: 2018-10-26T00:00:00Z
review text: Summary: Let \(H_V\) be a self-adjoint extension of the Schrödinger operator \(-\Delta+V(x)\) with the Dirichlet boundary condition on an arbitrary open set \(\Omega\) of \(\mathbb{R}^d\), where \(d\geq1\) and the negative part of potential \(V\) belongs to the Kato class on \(\Omega\). The purpose of this paper is to prove \(L^p\)-\(L^q\)-estimates and gradient estimates for an operator \(\varphi(H_V)\), where \(\varphi\) is an arbitrary rapidly decreasing function on \(\mathbb{R}\), and \(\varphi(H_V)\) is defined via the spectral theorem.
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 6966792
zbMATH Keywords: Schrödinger operators
zbMATH Keywords: functional calculus
zbMATH Keywords: Kato class
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/rmi/1024
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description: scientific article; zbMATH DE number 6966792