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]subset of R$[a,b]\subset {\mathbb {R}}$ and given an increasing divergent sequence dn$d_n$ of positive integers such that the derivative of order dn$d_n$ of f has a growth of the type Mdn$M_{d_n}$, when can we deduce that f is a function in the Denjoy-Carleman class CM([a,b])$C<^>M([a,b])$? We provide a positive result and show that a suitable condition on the gaps between the terms of the sequence dn$d_n$ is needed.

Albano P., Mughetti M. (2023). An interpolation problem in the Denjoy–Carleman classes. MATHEMATISCHE NACHRICHTEN, 296(3), 902-914 [10.1002/mana.202100122].

An interpolation problem in the Denjoy–Carleman classes

Albano P.;Mughetti M.
2023

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]subset of R$[a,b]\subset {\mathbb {R}}$ and given an increasing divergent sequence dn$d_n$ of positive integers such that the derivative of order dn$d_n$ of f has a growth of the type Mdn$M_{d_n}$, when can we deduce that f is a function in the Denjoy-Carleman class CM([a,b])$C<^>M([a,b])$? We provide a positive result and show that a suitable condition on the gaps between the terms of the sequence dn$d_n$ is needed.
2023
Albano P., Mughetti M. (2023). An interpolation problem in the Denjoy–Carleman classes. MATHEMATISCHE NACHRICHTEN, 296(3), 902-914 [10.1002/mana.202100122].
Albano P.; Mughetti M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/913313
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