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We are interested on families of formal power series in $(ℂ^{}, 0)$ parameterized by $ℂ^{n}$ ( $\hat{f} = \sum_{m = 0}^{\infty} P_{m} (x_{1}, \dots, x_{n}) x^{m}$ ). If every $P_{m}$ is a polynomial whose degree is bounded by a linear function ( $d e g P_{m} \leq A m + B$ for some $A > 0$ and $B \geq 0$ ) then the family is either convergent or the series $\hat{f} (c_{1}, \dots, c_{n}, x) \notin ℂ {x}$ for all $(c_{1}, \dots, c_{n}) \in ℂ^{n}$ except a pluri-polar set. Generalizations of these results are provided for formal objects associated to germs of diffeomorphism (formal power series, formal meromorphic functions, etc.). We are interested on describing the nature of the set of parameters where...

Holomorphic functions with singularities on algebraic sets.

Sičiak, Józef (2001)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

How to prove Fefferman's theorem without use of differential geometry

Ewa Ligocka (1981)

Annales Polonici Mathematici

Inégalités de Carleman et extension locale des fonctions holomorphes

M. Derridj (1982)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Interpolation by holomorphic functions in the unit ball with polynomial growth

Xavier Massaneda (1997)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Interpolation by Holomorphic Functions Smooth to the Boundary in the Unit Ball of Cn.

Joaquim Bruna, Joaquin Ma. Ortega (1986)

Mathematische Annalen

Interpolation on plane sets in C2

D. E. Papush, A. M. Russakovskii (1992)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Invariance for multiples of the twisted canonical bundle

Benoît Claudon (2007)

Annales de l’institut Fourier

Let $𝒳 \to Δ$ a smooth projective family and $(L, h)$ a pseudo-effective line bundle on $𝒳$ (i.e. with a non-negative curvature current $Θ h L$ ). In its works on invariance of plurigenera, Y.-T. Siu was interested in extending sections of $m K_{𝒳_{0}} + L$ (defined over the central fiber of the family $𝒳_{0}$ ) to sections of $m K_{𝒳} + L$ . In this article we consider the following problem: to extend sections of $m (K_{𝒳} + L)$ . More precisely, we show the following result: assuming the triviality of the multiplier ideal sheaf $ℐ (𝒳_{0}, h_{| 𝒳_{0}})$ , any section of $m (K_{𝒳_{0}} + L)$ extends to $𝒳$ ; in other...

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Holomorphic and Meromorphic Mappings and Curvature. II.

Holomorphic equivalence and proper mapping of bounded Reinhardt domains not containing the origin.

Holomorphic extension from the sphere to the ball in Hilbert space

Holomorphic extension of generalizations of $H^{p}$ functions.

Holomorphic extension of generalizations of $H^{p}$ functions. II.

Holomorphic extension to open hulls

Holomorphic extensions of formal objects

Holomorphic functions with singularities on algebraic sets.

How to prove Fefferman's theorem without use of differential geometry

Inégalités de Carleman et extension locale des fonctions holomorphes

Interpolation by holomorphic functions in the unit ball with polynomial growth

Interpolation by Holomorphic Functions Smooth to the Boundary in the Unit Ball of Cn.

Interpolation on plane sets in C2

Invariance for multiples of the twisted canonical bundle

Le principe de reflexion en des points de faible pseudo convexité, pour des applications holomorphes propres.

Le problème de Cauchy pour $\bar{\partial}$ -application

Le problème de Cauchy pour $\bar{\partial}$ et application

Levi flat hypersurfaces in $C^{2}$ with prescribed boundary : stability

Liouville's theorem for first-order partial differential operators

Localization of the Kobayashi Metric and the Boundary Continuity of Proper Holomorphic Mappings.

Currently displaying 101 – 120 of 218