Pré-Publication, Document De Travail Année : 2026

Short-time estimates for a real moment problem with two-term Weyl spectral law

Résumé

In this work, we first study the solvability of moment problems involving real exponentials $e^{\lambda_k t}$ and provide explicit estimates of the associated control cost. The result holds when the increasing sequence of distinct real numbers $(\lambda_k)_{k\in\mathbb{N}^*}$ satisfies a suitable two-term Weyl asymptotic law, without imposing any uniform spacing condition on blocks of its elements. We then deduce a corresponding controllability result for a linear control problem. Next, we present an exponential family fitting our hypotheses that cannot be treated by existing results of this type. Finally, we show how to deduce new exact controllability results for suitable fractional bilinear heat equations in higher-dimensional domains.

Fichier principal
Vignette du fichier
MomentGrowingBlocks.pdf (530.68 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-04622031 , version 1 (24-06-2024)
hal-04622031 , version 2 (12-05-2025)
hal-04622031 , version 3 (27-03-2026)

Licence

Identifiants

  • HAL Id : hal-04622031 , version 3

Citer

Rémi Buffe, Alessandro Duca. Short-time estimates for a real moment problem with two-term Weyl spectral law. 2026. ⟨hal-04622031v3⟩
520 Consultations
393 Téléchargements

Partager

  • More