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

Research output: Contribution to journal › Article

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 1
Externally published	Yes

Keywords

Lorentz spaces
Schrödinger equation
Wave operators

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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Georgiev, V., & Ivanov, A. (2005). Existence and mapping properties of the wave operator for the Schrödinger equation with singular potential. Proceedings of the American Mathematical Society, 133(7), 1993-2003. https://doi.org/10.1090/S0002-9939-05-07854-8

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AU - Ivanov, Angel

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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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