Boundedness of spectral multipliers for Schrödinger operators on open sets

Tsukasa Iwabuchi; Tokio Matsuyama; Koichi Taniguchi

doi:10.4171/rmi/1024

Boundedness of spectral multipliers for Schrödinger operators on open sets

Tsukasa Iwabuchi, Tokio Matsuyama, Koichi Taniguchi

Chuo University

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

Let HV be a self-adjoint extension of the Schrödinger operator −Δ + V (x) with the Dirichlet boundary condition on an arbitrary open set Ω of R^d, where d ≥ 1 and the negative part of potential V belongs to the Kato class on Ω. The purpose of this paper is to prove L^p-L^qestimates and gradient estimates for an operator ϕ(HV ), where ϕ is an arbitrary rapidly decreasing function on R, and ϕ(HV ) is defined via the spectral theorem.

Original language	English
Pages (from-to)	1277-1322
Number of pages	46
Journal	Revista Matematica Iberoamericana
Volume	34
Issue number	3
DOIs	https://doi.org/10.4171/rmi/1024
Publication status	Published - 2018

Keywords

Functional calculus
Kato class
Schrödinger operators

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title = "Boundedness of spectral multipliers for Schr{\"o}dinger operators on open sets",

abstract = "Let HV be a self-adjoint extension of the Schr{\"o}dinger operator −Δ + V (x) with the Dirichlet boundary condition on an arbitrary open set Ω of Rd, where d ≥ 1 and the negative part of potential V belongs to the Kato class on Ω. The purpose of this paper is to prove Lp-Lqestimates and gradient estimates for an operator ϕ(HV ), where ϕ is an arbitrary rapidly decreasing function on R, and ϕ(HV ) is defined via the spectral theorem.",

keywords = "Functional calculus, Kato class, Schr{\"o}dinger operators",

author = "Tsukasa Iwabuchi and Tokio Matsuyama and Koichi Taniguchi",

note = "Funding Information: The first author was supported by JSPS Grant-in-Aid for Young Scientists (B) (No. 25800069), Japan Society for the Promotion of Science. The second author was supported by Grant-in-Aid for Scientific Research (C) (No. 15K04967), Japan Society for the Promotion of Science. Publisher Copyright: {\textcopyright} European Mathematical Society.",

year = "2018",

doi = "10.4171/rmi/1024",

language = "English",

volume = "34",

pages = "1277--1322",

journal = "Revista Matematica Iberoamericana",

issn = "0213-2230",

publisher = "Universidad Autonoma de Madrid",

number = "3",

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TY - JOUR

T1 - Boundedness of spectral multipliers for Schrödinger operators on open sets

AU - Iwabuchi, Tsukasa

AU - Matsuyama, Tokio

AU - Taniguchi, Koichi

N1 - Funding Information: The first author was supported by JSPS Grant-in-Aid for Young Scientists (B) (No. 25800069), Japan Society for the Promotion of Science. The second author was supported by Grant-in-Aid for Scientific Research (C) (No. 15K04967), Japan Society for the Promotion of Science. Publisher Copyright: © European Mathematical Society.

PY - 2018

Y1 - 2018

N2 - Let HV be a self-adjoint extension of the Schrödinger operator −Δ + V (x) with the Dirichlet boundary condition on an arbitrary open set Ω of Rd, where d ≥ 1 and the negative part of potential V belongs to the Kato class on Ω. The purpose of this paper is to prove Lp-Lqestimates and gradient estimates for an operator ϕ(HV ), where ϕ is an arbitrary rapidly decreasing function on R, and ϕ(HV ) is defined via the spectral theorem.

AB - Let HV be a self-adjoint extension of the Schrödinger operator −Δ + V (x) with the Dirichlet boundary condition on an arbitrary open set Ω of Rd, where d ≥ 1 and the negative part of potential V belongs to the Kato class on Ω. The purpose of this paper is to prove Lp-Lqestimates and gradient estimates for an operator ϕ(HV ), where ϕ is an arbitrary rapidly decreasing function on R, and ϕ(HV ) is defined via the spectral theorem.

KW - Functional calculus

KW - Kato class

KW - Schrödinger operators

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U2 - 10.4171/rmi/1024

DO - 10.4171/rmi/1024

M3 - Article

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EP - 1322

JO - Revista Matematica Iberoamericana

JF - Revista Matematica Iberoamericana

IS - 3

ER -

Boundedness of spectral multipliers for Schrödinger operators on open sets

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