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Nazarov's Conjecture on Truncations for Fractional Laplacians

Analysis · posed by Alexander I. Nazarov, 2021 · solved

1 comment

Statement

Nazarov conjectured that for s∈(1,3/2)s \in (1, 3/2) the quadratic form of the spectral fractional Dirichlet Laplacian strictly increases under u↦∣u∣u \mapsto |u| when uu changes sign. Proved and substantially generalized, with the same conclusion for the restricted form.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Egor Ignatev, Alexander I. Nazarov, Pavel Nichitenko and Artur Tursunbaev, using Claude

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    From the paper: "The original proof of Corollary 3 via Lemma 5 (for m = 1) was given by the LLM Claude (Anthropic), which was directed jointly by E.I., P.N., and A.T." A named corollary, with the human direction credited by initials.

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