THE SCATTERING RESONANCES FOR SCHRODINGER-TYPE OPERATORS WITH UNBOUNDED POTENTIALS

被引：0

作者：

Li, Peijun ^{[1
,2
]}

Yao, Xiaohua ^{[3
,4
]}

Zhao, Yue ^{[3
,4
]}

机构：

[1] Acad Math & Syst Sci, Chinese Acad Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China

[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

[3] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China

[4] Cent China Normal Univ, Key Lab NAA MOE, Wuhan 430079, Peoples R China

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2024年 / 56卷 / 02期

关键词：

scattering resonances; Schrodinger operator; fractional Schrodinger operator; unbounded potentials; meromorphic continuation; resolvent estimates; UNIQUE CONTINUATION; POSITIVE EIGENVALUES; SOBOLEV; EXPANSIONS; ABSENCE;

D O I：

10.1137/22M14986191

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper addresses the meromorphic continuation of the outgoing resolvent associated with Schrodinger-type operators in three dimensions. The first part focuses on the classical Schrodinger-type operator involving unbounded potentials. The absence of nonzero real poles for the outgoing resolvent is investigated. The second part examines the fractional Schrodinger operator, including both bounded and unbounded potentials. The analysis relies on a resolvent identity that establishes a connection between the resolvents of the fractional Schrodinger operator and its classical counterpart.

引用

页码：2149 / 2170

页数：22

共 36 条

[1]

[Anonymous], 1975, ANN SC NORM SUPER PI, P151

[2] On Lp-Resolvent Estimates and the Density of Eigenvalues for Compact Riemannian Manifolds [J].