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

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3 Citations (Scopus)

Abstract

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 Hv s in the case 0 ≤ s < 3/2.

Original languageEnglish
Pages (from-to)1993-2003
Number of pages11
JournalProceedings of the American Mathematical Society
Volume133
Issue number7
DOIs
Publication statusPublished - 2005 Jul
Externally publishedYes

Fingerprint

Sobolev spaces
Singular Potential
Wave Operator
Lorentz Spaces
Homogeneous Space
Sobolev Spaces
Equivalence
Three-dimensional
Estimate

Keywords

  • Lorentz spaces
  • Schrödinger equation
  • Wave operators

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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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 Hv s in the case 0 ≤ s < 3/2.",
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AU - Gueorguiev, Vladimir Simeonov

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 Hv s 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 Hv s in the case 0 ≤ s < 3/2.

KW - Lorentz spaces

KW - Schrödinger equation

KW - Wave operators

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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