Pith. sign in

REVIEW 3 cited by

Spectral Inequalities for the Schr{\"o}dinger operator

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1901.03513 v1 pith:5FCASDRN submitted 2019-01-11 math.AP

classification math.AP
keywords operatorspectralanalyticdeltaequationinequalitiesmetricschr
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

In this paper we deal with the so-called "spectral inequalities", which yield a sharp quantification of the unique continuation for the spectral family associated with the Schr\"odinger operator in $ \mathbb{R}^d$ \begin{equation*} H_{g,V} = \Delta_g + V(x), \end{equation*} where $\Delta_g$ is the Laplace-Beltrami operator with respect to an analytic metric $g$, which is a perturbation of the Euclidean metric, and $V(x)$ a real valued analytic potential vanishing at infinity.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Optimal geometric barriers for weighted observability of heat semigroups on metric measure spaces

    math.AP 2026-07 accept novelty 8.0 of 10

    If a heat-observability inequality with weight h holds from a set ω, then h(t) decays at least like exp(-κ L(ω)²/t) for every κ<1/2, yielding the sharp lower bound γ≥L(ω)²/2.

  2. Quantitative uniqueness properties for functions on compact quasi-analytic manifolds

    math.FA 2026-06 unverdicted novelty 6.0 of 10

    Quantitative uniqueness and observability theorems for quasi-analytic functions on compact manifolds, generalizing Logvinenko-Sereda results and Kukavica-Li to infinite sums with energy decay.

  3. Sampling and equidistribution theorems for elliptic second order operators, lifting of eigenvalues, and applications

    math.AP 2025-05 conditional novelty 3.0 of 10

    Tautenhahn and Veselic correct an error in their 2020 proof and establish scale-free sampling and equidistribution estimates for eigenfunctions of elliptic second order operators with Lipschitz coefficients.

Pith tools