Power substitution in quasianalytic Carleman classes

Lev Buhovsky; Avner Kiro; Sasha Sodin

doi:10.1007/s11856-019-1949-4

Power substitution in quasianalytic Carleman classes

Lev Buhovsky, Avner Kiro, Sasha Sodin

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

Consider an equation of the form f(x) = g(x^k), 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 language	English
Pages (from-to)	79-90
Number of pages	12
Journal	Israel Journal of Mathematics
Volume	235
Issue number	1
Early online date	5 Nov 2019
DOIs	https://doi.org/10.1007/s11856-019-1949-4
State	Published - 1 Jan 2020

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11856-019-1949-4

http://arxiv.org/abs/1802.09443License: Other

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title = "Power substitution in quasianalytic Carleman classes",

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.",

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Power substitution in quasianalytic Carleman classes

Abstract

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