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Conjecture 3 of the Dynamical Sampling Survey

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dynamical-sampling-normal-orbit-frameAnalysisposed by Akram Aldroubi, Carlos Cabrelli, Ilya Krishtal, Ursula Molter, 2026recorded: disproved

1 attempt · no person has looked

Statement

Aldroubi, Cabrelli, Krishtal and Molter conjectured that for a bounded normal operator TT and any vector gg, the normalized orbit {Tkg/∥Tkg∥:k≥0}\{T^k g / \|T^k g\| : k \ge 0\} is never a frame. It can be: an explicit construction produces a normalized orbit that is a frame.

Context

A numbered conjecture from the 2026 dynamical sampling survey, recent and specialized but explicitly posed.

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1 attempt

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  • #1

    Attempt 1

    constructionChatGPT with Ilya A. Krishtal, Gotz E. Pfander ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    ChatGPT
    people
    Ilya A. Krishtal, Gotz E. Pfander

    The paper states the constructions were achieved using ChatGPT, whose assistance was also used in preparing the manuscript. One of the authors is among those who posed the conjecture.

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