Hulls of subsets of the torus in ${\mathbb {C}}^2$

Herbert Alexander

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Families of analytic discs in $𝐂^{n}$ with boundaries on a prescribed $C R$ submanifold

C. Denson Hill, Geraldine Taiani (1978)

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Closures of open analytic polyhedra

P. J. de Paepe (1974)

Compositio Mathematica

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An embedding theorem for real analytic spaces

F. Acquistapace, F. Broglia, A. Tognoli (1979)

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Analytic functions in general analysis

Angus E. Taylor (1937)

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Approximation of $C^{\infty}$ -functions without changing their zero-set

F. Broglia, A. Tognoli (1989)

Annales de l'institut Fourier

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For a $C^{\infty}$ function $ϕ : M \to ℝ$ (where $M$ is a real algebraic manifold) the following problem is studied. If $ϕ^{- 1} (0)$ is an algebraic subvariety of $M$ , can $ϕ$ be approximated by rational regular functions $f$ such that $f^{- 1} (0) = ϕ^{- 1} (0) ?$ We find that this is possible if and only if there exists a rational regular function $g : M \to ℝ$ such that $g^{- 1} (0) = ϕ^{- 1} (0)$ and g(x) $\cdot ϕ (x) \geq 0$ for any $x$ in $ℝ^{n}$ . Similar results are obtained also in the analytic and in the Nash cases. For non approximable functions the minimal flatness locus...

A local factorization of analytic functions and its applications

E. Ligocka (1973)

Studia Mathematica

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Displaying similar documents to “Hulls of subsets of the torus in ℂ 2 ”

Families of analytic discs in 𝐂 n with boundaries on a prescribed C R submanifold

Closures of open analytic polyhedra

An embedding theorem for real analytic spaces

Analytic functions in general analysis

Approximation of C ∞ -functions without changing their zero-set

A local factorization of analytic functions and its applications

Displaying similar documents to “Hulls of subsets of the torus in $ℂ^{2}$ ”

Families of analytic discs in $𝐂^{n}$ with boundaries on a prescribed $C R$ submanifold

Approximation of $C^{\infty}$ -functions without changing their zero-set