Existence and mapping properties of the wave operator for the Schrödinger equation with singular potential

Vladimir Georgiev; Angel Ivanov

doi:10.1090/S0002-9939-05-07854-8

Existence and mapping properties of the wave operator for the Schrödinger equation with singular potential

Vladimir Georgiev^*, Angel Ivanov

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

We consider the Schrödinger equation in three-dimensional space with small potential in the Lorentz space L^3/2,∞ and we prove Strichartz-type estimates for the solution to this equation. Moreover, using Cook's method, we prove the existence of the wave operator. In the last section we prove the equivalence between the homogeneous Sobolev spaces H^s and H_v^s in the case 0 ≤ s < 3/2.

Original language	English
Pages (from-to)	1993-2003
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	133
Issue number	7
DOIs	https://doi.org/10.1090/S0002-9939-05-07854-8
Publication status	Published - 2005 Jul
Externally published	Yes

Keywords

Lorentz spaces
Schrödinger equation
Wave operators

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-05-07854-8

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abstract = "We consider the Schr{\"o}dinger equation in three-dimensional space with small potential in the Lorentz space L3/2,∞ and we prove Strichartz-type estimates for the solution to this equation. Moreover, using Cook's method, we prove the existence of the wave operator. In the last section we prove the equivalence between the homogeneous Sobolev spaces Hs and Hvs in the case 0 ≤ s < 3/2.",

keywords = "Lorentz spaces, Schr{\"o}dinger equation, Wave operators",

author = "Vladimir Georgiev and Angel Ivanov",

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T1 - Existence and mapping properties of the wave operator for the Schrödinger equation with singular potential

AU - Georgiev, Vladimir

AU - Ivanov, Angel

PY - 2005/7

Y1 - 2005/7

N2 - We consider the Schrödinger equation in three-dimensional space with small potential in the Lorentz space L3/2,∞ and we prove Strichartz-type estimates for the solution to this equation. Moreover, using Cook's method, we prove the existence of the wave operator. In the last section we prove the equivalence between the homogeneous Sobolev spaces Hs and Hvs in the case 0 ≤ s < 3/2.

AB - We consider the Schrödinger equation in three-dimensional space with small potential in the Lorentz space L3/2,∞ and we prove Strichartz-type estimates for the solution to this equation. Moreover, using Cook's method, we prove the existence of the wave operator. In the last section we prove the equivalence between the homogeneous Sobolev spaces Hs and Hvs in the case 0 ≤ s < 3/2.

KW - Lorentz spaces

KW - Schrödinger equation

KW - Wave operators

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DO - 10.1090/S0002-9939-05-07854-8

M3 - Article

AN - SCOPUS:22544441593

VL - 133

SP - 1993

EP - 2003

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 7

ER -

Existence and mapping properties of the wave operator for the Schrödinger equation with singular potential

Abstract

Keywords

ASJC Scopus subject areas

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