Semiclassical resolvent bound for compactly supported L1 potentials

Jacob Shapiro

doi:10.4171/JST/308

Semiclassical resolvent bound for compactly supported L¹ potentials

Jacob Shapiro

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

9 Citations (Scopus)

Abstract

We give an elementary proof of a weighted resolvent estimate for semiclassical Schrödinger operators in dimension n 1. We require the potential belong to L¹.Rⁿ/ and have compact support, but do not require that it have distributional derivatives in L¹.Rⁿ/. The weighted resolvent norm is bounded by e^C h^{4=3 log.h1/}, where h is the semiclassical parameter.

Original language	English
Pages (from-to)	651-672
Number of pages	22
Journal	Journal of Spectral Theory
Volume	10
Issue number	2
DOIs	https://doi.org/10.4171/JST/308
Publication status	Published - 2020

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title = "Semiclassical resolvent bound for compactly supported L1 potentials",

abstract = "We give an elementary proof of a weighted resolvent estimate for semiclassical Schr{\"o}dinger operators in dimension n 1. We require the potential belong to L1.Rn/ and have compact support, but do not require that it have distributional derivatives in L1.Rn/. The weighted resolvent norm is bounded by eC h4=3 log.h1/, where h is the semiclassical parameter.",

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author = "Jacob Shapiro",

note = "Publisher Copyright: {\textcopyright} European Mathematical Society.",

year = "2020",

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N1 - Publisher Copyright: © European Mathematical Society.

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AB - We give an elementary proof of a weighted resolvent estimate for semiclassical Schrödinger operators in dimension n 1. We require the potential belong to L1.Rn/ and have compact support, but do not require that it have distributional derivatives in L1.Rn/. The weighted resolvent norm is bounded by eC h4=3 log.h1/, where h is the semiclassical parameter.

KW - Potential

KW - Resolvent

KW - Semi-classical

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DO - 10.4171/JST/308

M3 - Article

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SP - 651

EP - 672

JO - Journal of Spectral Theory

JF - Journal of Spectral Theory

IS - 2

ER -

Semiclassical resolvent bound for compactly supported L¹ potentials

Abstract

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