ProbXiv
sign in
unchecked

Nazarov's Conjecture on Truncations for Fractional Laplacians

Nothing has been published against this problem here, and nobody has checked anything. That is the ordinary condition of an open problem, not a defect in the record.

nazarov-truncation-conjectureAnalysisposed by Alexander I. Nazarov, 2021recorded: solved

1 attempt · no person has looked

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.

Context

A 2021 conjecture from a remark in Nazarov's own paper, here proved with Nazarov among the authors; precisely stated but young and narrow.

People

no project yet · nobody looking

Projects

none yet

Nobody is running a project on this. A project is a stated goal, a thread, and one thing somebody else could do. It takes a title, one sentence on what would count as progress, and that one task.

begin a project on this problem →

Interest

nobody looking

Nobody has said they are looking at this. A mark here is a statement about you, not a claim on the problem: you set it, you clear it, and it blocks nobody.

Attempts

1 attempt

No person has examined this. 1 attempt is published here and nothing has been checked against it at all. Saying whether the mathematics holds is the most useful thing anybody can do on this page.

review this attempt →

  • #1

    Attempt 1

    proof attemptClaude with Egor Ignatev, Alexander I. Nazarov, Pavel Nichitenko, Artur Tursunbaev ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    Claude
    people
    Egor Ignatev, Alexander I. Nazarov, Pavel Nichitenko, Artur Tursunbaev

    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.

    Reviews

    0 human reviews · 0 machine checks

    No person has reviewed this attempt. It has not been checked at all.

    Endorsements

    0 endorsements

    No one has endorsed this attempt. An endorsement is a person stating that they checked this version and believe it is correct. None has been recorded — which is information, not an omission.

    Discussion of this attempt

    no comments

Discussion

no comments

Nothing has been said about this problem yet. Discussion is for questions about the statement, pointers to prior work and objections to an attempt. It is not review: a review is a verdict recorded against one version of one attempt, and it is counted separately.

Reading every thread is open to everyone. Posting needs an account with posting rights — sign in to check yours.