Nonlinear conditions for ultradifferentiability: a uniform approach (2024)

Schindl, G., Nenning, D. N. (2022). Nonlinear conditions for ultradifferentiability: a uniform approach. Journal of Geometric Analysis, 32(6), [171]. https://doi.org/10.1007/s12220-022-00914-2

Schindl, Gerhard ; Nenning, David Nicolas ; Rainer, Armin. / Nonlinear conditions for ultradifferentiability: a uniform approach. in: Journal of Geometric Analysis. 2022 ; Band 32, Nr. 6.

@article{dd0c56a7c65149ae8766472b47c3b54c,

title = "Nonlinear conditions for ultradifferentiability: a uniform approach",

abstract = "Recent work showed that a theorem of Joris (that a function f is smooth if two coprime powers of f are smooth) is valid in a wide variety of ultradifferentiable classes C. The core of the proof was essentially 1 dimensional. In certain cases, a multidimensional version resulted from subtle reduction arguments, but general validity, notably in the quasianalytic setting, remained open. In this paper, we give a uniform proof which works in all cases and dimensions. It yields the result even on infinite-dimensional Banach spaces and convenient vector spaces. We also consider more general nonlinear conditions, namely general analytic germs Φ instead of the powers and characterize when Φ ∘ f∈ C implies f∈ C.",

keywords = "Almost analytic extension, Holomorphic approximation, Joris theorem, Pseudo-immersion, Quasianalytic and non-quasianalytic, Ultradifferentiable classes",

author = "Gerhard Schindl and Nenning, {David Nicolas} and Armin Rainer",

note = "Publisher Copyright: {\textcopyright} 2022, Mathematica Josephina, Inc.",

year = "2022",

month = mar,

day = "26",

doi = "10.1007/s12220-022-00914-2",

language = "English",

volume = "32",

journal = "Journal of Geometric Analysis",

issn = "1050-6926",

number = "6",

}

Schindl, G, Nenning, DN 2022, 'Nonlinear conditions for ultradifferentiability: a uniform approach', Journal of Geometric Analysis, Jg. 32, Nr. 6, 171. https://doi.org/10.1007/s12220-022-00914-2

Nonlinear conditions for ultradifferentiability: a uniform approach. / Schindl, Gerhard; Nenning, David Nicolas; Rainer, Armin.

in: Journal of Geometric Analysis, Band 32, Nr. 6, 171, 26.03.2022.

Veröffentlichungen: Beitrag in Fachzeitschrift › Artikel › Peer Reviewed

TY - JOUR

T1 - Nonlinear conditions for ultradifferentiability: a uniform approach

AU - Schindl, Gerhard

AU - Nenning, David Nicolas

AU - Rainer, Armin

N1 - Publisher Copyright:© 2022, Mathematica Josephina, Inc.

PY - 2022/3/26

Y1 - 2022/3/26

N2 - Recent work showed that a theorem of Joris (that a function f is smooth if two coprime powers of f are smooth) is valid in a wide variety of ultradifferentiable classes C. The core of the proof was essentially 1 dimensional. In certain cases, a multidimensional version resulted from subtle reduction arguments, but general validity, notably in the quasianalytic setting, remained open. In this paper, we give a uniform proof which works in all cases and dimensions. It yields the result even on infinite-dimensional Banach spaces and convenient vector spaces. We also consider more general nonlinear conditions, namely general analytic germs Φ instead of the powers and characterize when Φ ∘ f∈ C implies f∈ C.

AB - Recent work showed that a theorem of Joris (that a function f is smooth if two coprime powers of f are smooth) is valid in a wide variety of ultradifferentiable classes C. The core of the proof was essentially 1 dimensional. In certain cases, a multidimensional version resulted from subtle reduction arguments, but general validity, notably in the quasianalytic setting, remained open. In this paper, we give a uniform proof which works in all cases and dimensions. It yields the result even on infinite-dimensional Banach spaces and convenient vector spaces. We also consider more general nonlinear conditions, namely general analytic germs Φ instead of the powers and characterize when Φ ∘ f∈ C implies f∈ C.

KW - Almost analytic extension

KW - Holomorphic approximation

KW - Joris theorem

KW - Pseudo-immersion

KW - Quasianalytic and non-quasianalytic

KW - Ultradifferentiable classes

UR - http://www.scopus.com/inward/record.url?scp=85127222319&partnerID=8YFLogxK

U2 - 10.1007/s12220-022-00914-2

DO - 10.1007/s12220-022-00914-2

M3 - Article

VL - 32

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

SN - 1050-6926

IS - 6

M1 - 171

ER -

Schindl G, Nenning DN, Rainer A. Nonlinear conditions for ultradifferentiability: a uniform approach. Journal of Geometric Analysis. 2022 Mär 26;32(6):171. doi: 10.1007/s12220-022-00914-2