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Sharp Lieb-Thirring Inequalities in High Dimensions

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A. Laptev, T. Weidl

Mathematical Physics · Submitted 3 Mar 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show how a matrix version of the Buslaev-Faddeev-Zakharov trace formulae for a one-dimensional Schr\"odinger operator leads to Lieb-Thirring inequalities with sharp constants $L^{cl}_{\gamma,d}$ with $\gamma\ge 3/2$ and arbitrary $d\ge 1$.

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arXiv IDmath-ph/9903007 (version 2)
Pith IDR553X4WU, Pith's permanent record of this paper and its review
CitationA. Laptev, T. Weidl. "Sharp Lieb-Thirring Inequalities in High Dimensions." arXiv:math-ph/9903007 (1999). https://pith.science/paper/R553X4WU
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,321 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.77 · compares with prior results 0.19 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We show how a matrix version of the Buslaev-Faddeev-Zakharov trace formulae for a one-dimensional Schr\"odinger operator leads to Lieb-Thirring inequalities with sharp constants $L^{cl}_{\gamma,d}$ with $\gamma\ge 3/2$ and arbitrary $d\ge 1$. (revised, to appear in Acta Math)

background contribution method result interpretation main claim

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We show how a matrix version of the Buslaev-Faddeev-Zakharov trace formulae for a one-dimensional Schr\"odinger operator leads to Lieb-Thirring inequalities with sharp constants $L^{cl}_{\gamma,d}$ with $\gamma\ge 3/2$ and arbitrary $d\ge 1$. contribution 0.59 0.94 0.94 asserted 1.00
s1 (revised, to appear in Acta Math) background 0.77 0.04 0.02 unclear 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We show how a matrix version of the Buslaev-Faddeev-Zakharov trace formulae for a one-dimensional Schr\"odinger operator leads to Lieb-Thirring inequalities with sharp constants $L^{cl}_{\gamma,d}$ with $\gamma\ge 3/2$ and arbitrary $d\ge 1$. (revised, to appear in Acta Math)

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