Extended Gevrey regularity via weighted matrices

2022/09/01 by Nenad Teofanov, Teofanov, Nenad, Filip Tomić +1 · 2 citations
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2209.00457

openalex publication_date 2022/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main aim of this paper is to compare two recent approaches for investigating the interspace between the union of Gevrey spaces \mathcal G_t (U) and the space of smooth functions C^∞(U). The first approach in the style of Komatsu is based on the properties of two parameter sequences M_p=p^τpσ, τ>0, σ>1. The other one uses weight matrices defined by certain weight functions. We prove the equivalence of the corresponding spaces in the Beurling case by taking projective limits with respect to matrix parameters, while in the Roumieu case we need to consider a larger space then the one obtained as the inductive limit of extended Gevrey classes.

Cited by

• Extending wavelet regularity beyond Gevrey classes
• Surjectivity of the asymptotic Borel map in Carleman ultraholomorphic classes defined by sequences with shifted moments

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