Global estimates of fundamental solutions for higher-order Schrodinger equations

被引：17

作者：

Kim, JinMyong ^{[1
,2
]}

Arnold, Anton ^{[2
]}

Yao, Xiaohua ^{[3
]}

机构：

[1] Kim Il Sung Univ, Dept Math, Pyongyang, North Korea

[2] Vienna Univ Technol, Inst Anal & Sci Comp, A-1040 Vienna, Austria

[3] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China

来源：

MONATSHEFTE FUR MATHEMATIK | 2012年 / 168卷 / 02期

关键词：

Oscillatory integral; Higher-order Schrodinger equation; Fundamental solution estimate; OSCILLATORY INTEGRALS;

D O I：

10.1007/s00605-011-0350-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we first establish global pointwise time-space estimates of the fundamental solution for Schrodinger equations, where the symbol of the spatial operator is a real non-degenerate elliptic polynomial. Then we use such estimates to establish related L (p) -L (q) estimates on the Schrodinger solution. These estimates extend known results from the literature and are sharp. This result was lately already generalized to a degenerate case (cf. [4]).

引用

页码：253 / 266

页数：14

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