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Landis' conjecture: a survey

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arxiv 2412.00788 v2 pith:GUIMLPPE submitted 2024-12-01 math.AP

Aingeru Fernández-Bertolin , Diana Stan , Luz Roncal This is my paper · ORCID
classification math.AP
keywords conjecturesurveyaccountadvancescloselycomplementconnectedcontexts
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We survey Kondrat'ev--Landis' conjecture, providing an up-to-date account of the main advances and describing the techniques developed. We complement the overview with references and formulations of the problem in further closely connected contexts.

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Cited by 2 Pith papers

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  1. On Support Cardinality for the Discrete Schr\"odinger Equation

    math-ph 2026-06 unverdicted novelty 6.0 of 10

    Minimal support cardinality S_d(N) of nontrivial origin-nonzero Dirichlet solutions is nondecreasing in d, so S_4(N) ≳ N²/log N, matching even-dimensional constructions up to a log factor.

  2. An optimal fractional Hardy inequality on the discrete half-line

    math.AP 2025-07 conditional novelty 6.0 of 10

    For σ in (0,1], the paper constructs an explicit optimal Hardy weight W^op_σ for (-Δ_N)^σ, with W^op_σ(n) approximately n^{-2σ} and an upper bound C_σ for the best constant in the n^{-2σ} Hardy inequality.

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