Continuous linear division and extension of \(C^\infty\) functions

DOI10.1215/S0012-7094-83-05011-1zbMath0521.32008MaRDI QIDQ1055588

Edward Bierstone, Gerald W. Schwarz

Publication date: 1983

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

division theoremsanalytic mapssubanalytic setextension theoremsreal analytic manifoldHironaka rectilinearization theoremlifting theoremsNash subanalytic set

Mathematics Subject Classification ID

Continuation of analytic objects in several complex variables (32D15) Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) Topological linear spaces of continuous, differentiable or analytic functions (46E10) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20) Locally convex Fréchet spaces and (DF)-spaces (46A04) Semi-analytic sets, subanalytic sets, and generalizations (32B20) Manifolds of mappings (58D15) Real-analytic and Nash manifolds (58A07) Algebras of holomorphic functions of several complex variables (32A38) Real-analytic manifolds, real-analytic spaces (32C05)

Related Items (27)

Semi-analyticité et sous-analyticité. (Semi-analyticity and sub- analyticity) ⋮ Global smoothing of a subanalytic set ⋮ Relations among analytic functions. I ⋮ Point réguliers d'un sous-analytique. (Regular points of a subanalytic set) ⋮ Distributions of corank 1 and their characteristic vector fields ⋮ Quelques résultats sur les ensembles Nash sous-analytiques ⋮ Local analytic invariants and splitting theorems in differential analysis ⋮ Polynomial inequalities, o-minimality and Denjoy-Carleman classes ⋮ Spectral multipliers on 2-step stratified groups. II ⋮ Deformation quantization and homological reduction of a lattice gauge model ⋮ Real roots of polynomials and right inverses for partial differential operators in the space of tempered distributions ⋮ Composition operators with closed range for one-dimensional smooth symbols ⋮ Spectral multipliers on 2-step stratified groups. I. ⋮ Some examples of \(C^\infty\) extension by linear operators ⋮ Invariance under the dihedral group and application to bifurcation problems ⋮ Characterization of splitting for Fréchet--Hilbert spaces via interpolation ⋮ Exterior multiplication with singularities: a Saito theorem in vector bundles ⋮ On Gabrielov's regularity condition for analytic mappings ⋮ Extension operators for real analytic functions on compact subvarieties of ⋮ Composite differentiable functions ⋮ \( \mathcal{C}^m\) solutions of semialgebraic or definable equations ⋮ Characterization of composition operators with closed range for one-dimensional smooth symbols ⋮ A proof of A. Gabrielov's rank theorem ⋮ On the existence of star products on quotient spaces of linear Hamiltonian torus actions ⋮ On covariant functions and distributions under the action of a compact group ⋮ Invariant Whitney functions ⋮ Examples of compact sets with non-empty interior which do not admit a continuous linear extension operator for ultradifferentiable functions of Beurling type

Cites Work

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