Dispersion estimates for one-dimensional Schrodinger and Klein-Gordon equations revisited

被引：12

作者：

Egorova, I. E. ^{[1
]}

Kopylova, E. A. ^{[2
,3
]}

Marchenko, V. A. ^{[1
]}

Teschl, G. ^{[2
,4
]}

机构：

[1] B Verkin Inst Low Temp Phys, Kharkov, Ukraine

[2] Univ Vienna, Vienna, Austria

[3] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow, Russia

[4] Int Erwin Schrodinger Inst Math Phys, Vienna, Austria

来源：

RUSSIAN MATHEMATICAL SURVEYS | 2016年 / 71卷 / 03期

基金：

奥地利科学基金会;

关键词：

Schrodinger equation; Klein-Gordon equation; dispersion estimates; scattering; INVERSE SCATTERING; ASYMPTOTIC EXPANSIONS; WAVE-EQUATIONS; LINE; OPERATORS;

D O I：

10.1070/RM9708

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that for a one-dimensional Schrodinger operator with a potential whose first moment is integrable the elements of the scattering matrix are in the unital Wiener algebra of functions with integrable Fourier transforms. This is then used to derive dispersion estimates for solutions of the associated Schrodinger and Klein-Gordon equations. In particular, the additional decay conditions are removed in the case where a resonance is present at the edge of the continuous spectrum.

引用

页码：391 / 415

页数：25

共 29 条

[1]

[Anonymous], HOKKAIDO MATH J, DOI 10.14492/hokmj/1249046361

[2]

[Anonymous], 2010, Handbook of Mathematical Functions

[3] On asymptotic stability of solitary waves for nonlinear Schrodinger equations [J].