Approximation theorems and Nash conjecture

Alberto Tognoli

Displaying similar documents to “Approximation theorems and Nash conjecture”

On the relative Nash approximation of analytic maps.

Alberto Tancredi, Alberto Tognoli (1998)

Revista Matemática Complutense

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An embedding theorem for real analytic spaces

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

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Almost Analytic Local Algebraicity of Analytic Sets and Functions.

Michael A. Buchner, W. Kucharz (1987)

Mathematische Zeitschrift

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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...

Analytic curves in power series rings

Herwig Hauser, Gerd Müller (1990)

Compositio Mathematica

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On real algebraic links in $S^{3}$

R. Benedetti, M. Shiota (1998)

Bollettino dell'Unione Matematica Italiana

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Viene presentata una costruzione che, dato un arbitrario nodo $L \subseteq S^{3}$ , produce allo stesso tempo: 1) un'applicazione polinomiale $f : (R^{4}, 0) \to (R^{2}, 0)$ con singolarità (debolmente) isolata in $0$ e $L$ come tipo di nodo della singolarità; 2) una risoluzione delle singolarità di $f$ nel senso di Hironaka. Specializzando la costruzione ai nodi fibrati otteniamo una versione debole (a meno di scoppiementi e nella categoria analitica reale) di un reciproco per il teorema di fibrazione di Milnor.

Semianalytic and subanalytic sets

Edward Bierstone, Pierre D. Milman (1988)

Publications Mathématiques de l'IHÉS

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Displaying similar documents to “Approximation theorems and Nash conjecture”

On the relative Nash approximation of analytic maps.

An embedding theorem for real analytic spaces

Almost Analytic Local Algebraicity of Analytic Sets and Functions.

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

Analytic curves in power series rings

On real algebraic links in S 3

Semianalytic and subanalytic sets

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

On real algebraic links in $S^{3}$