Generalized Fourier Transform for Schrödinger Operators with Potentials of Order Zero

Shmuel Agmon; Jaime Cruz-Sampedro; Ira Herbst

doi:10.1006/jfan.1999.3432

Generalized Fourier Transform for Schrödinger Operators with Potentials of Order Zero

Shmuel Agmon^*
, Jaime Cruz-Sampedro
, Ira Herbst

^*Corresponding author for this work

Einstein Institute of Mathematics

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

21 Scopus citations

Abstract

We investigate the Schrödinger operator H=-Δ+V acting in L²(Rⁿ), n≥2, for potentials V that satisfy ∂^α_xV(x)=O(x^-α) as x→∞. By introducing coordinates on Rⁿ closely related to a relevant eikonal equation we obtain an eigenfunction expansion for H at high energies.

Original language	English
Pages (from-to)	345-369
Number of pages	25
Journal	Journal of Functional Analysis
Volume	167
Issue number	2
DOIs	https://doi.org/10.1006/jfan.1999.3432
State	Published - 1 Oct 1999

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title = "Generalized Fourier Transform for Schr{\"o}dinger Operators with Potentials of Order Zero",

abstract = "We investigate the Schr{\"o}dinger operator H=-Δ+V acting in L2(Rn), n≥2, for potentials V that satisfy ∂αxV(x)=O(x-α) as x→∞. By introducing coordinates on Rn closely related to a relevant eikonal equation we obtain an eigenfunction expansion for H at high energies.",

author = "Shmuel Agmon and Jaime Cruz-Sampedro and Ira Herbst",

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AU - Cruz-Sampedro, Jaime

AU - Herbst, Ira

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N2 - We investigate the Schrödinger operator H=-Δ+V acting in L2(Rn), n≥2, for potentials V that satisfy ∂αxV(x)=O(x-α) as x→∞. By introducing coordinates on Rn closely related to a relevant eikonal equation we obtain an eigenfunction expansion for H at high energies.

AB - We investigate the Schrödinger operator H=-Δ+V acting in L2(Rn), n≥2, for potentials V that satisfy ∂αxV(x)=O(x-α) as x→∞. By introducing coordinates on Rn closely related to a relevant eikonal equation we obtain an eigenfunction expansion for H at high energies.

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SP - 345

EP - 369

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

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Generalized Fourier Transform for Schrödinger Operators with Potentials of Order Zero

Abstract

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