Power substitution in quasianalytic Carleman classes

Lev Buhovsky, Avner Kiro*, Sasha Sodin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Consider an equation of the form f(x) = g(xk), where k > 1 is an integer and f(x) is a function in a given Carleman class of smooth functions. For each k, we construct a non-homogeneous Carleman-type class which contains all the smooth solutions g(x) to such equations. We prove that if the original Carleman class is quasianalytic, then so is the new class. The results admit an extension to multivariate functions.

Original languageEnglish
Pages (from-to)79-90
Number of pages12
JournalIsrael Journal of Mathematics
Volume235
Issue number1
DOIs
StatePublished - 1 Jan 2020

Funding

FundersFunder number
Hebrew University Magnes Press
Horizon 2020 Framework Programme639305, 757585, 692616

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