An interpolation problem in the Denjoy-Carleman classes

2021/12/06 by Paolo G. Albano, Albano, Paolo, Marco Mughetti +1
Mathematics · #26E05 #26E10 #41A17 #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2112.03180

openalex publication_date 2021/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Inspired by some iterative algorithms useful for proving the real analyticity (or the Gevrey regularity) of a solution of a linear partial differential equation with real-analytic coefficients, we consider the following question. Given a smooth function defined on [a,b]⊂ℝ and given an increasing divergent sequence d_n of positive integers such that the derivative of order d_n of f has a growth of the type M_dn, when can we deduce that f is a function in the Denjoy-Carleman class C^M([a,b])? We provide a positive result, and we show that a suitable condition on the gaps between the terms of the sequence d_n is needed.

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