Effective local finite generation of multiplier ideal sheaves

Dan Popovici

Displaying similar documents to “Effective local finite generation of multiplier ideal sheaves”

On microlocal analyticity of solutions of first-order nonlinear PDE

Shif Berhanu (2009)

Annales de l’institut Fourier

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We study the microlocal analyticity of solutions $u$ of the nonlinear equation $u_{t} = f (x, t, u, u_{x})$ where $f (x, t, ζ_{0}, ζ)$ is complex-valued, real analytic in all its arguments and holomorphic in $(ζ_{0}, ζ)$ . We show that if the function $u$ is a $C^{2}$ solution, $σ \in Char L^{u}$ and $\frac{1}{i} σ ([L^{u}, \bar{L^{u}}]) < 0$ or if $u$ is a $C^{3}$ solution, $σ \in Char L^{u}$ , $σ ([L^{u}, \bar{L^{u}}]) = 0$ , and $σ ([L^{u}, [L^{u}, \bar{L^{u}}]]) \neq 0$ , then $σ \notin W F_{a} u$ . Here $W F_{a} u$ denotes the analytic wave-front set of $u$ and Char $L^{u}$ is the characteristic set of the linearized operator. When $m = 1$ , we prove a more general result involving the repeated brackets of $L^{u}$ and $\bar{L^{u}}$ of any...

Embedding theorems for Müntz spaces

Isabelle Chalendar, Emmanuel Fricain, Dan Timotin (2011)

Annales de l’institut Fourier

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We discuss boundedness and compactness properties of the embedding $M_{Λ}^{1} \subset L^{1} (μ)$ , where $M_{Λ}^{1}$ is the closed linear span of the monomials $x^{λ_{n}}$ in $L^{1} ([0, 1])$ and $μ$ is a finite positive Borel measure on the interval $[0, 1]$ . In particular, we introduce a class of “sublinear” measures and provide a rather complete solution of the embedding problem for the class of quasilacunary sequences $Λ$ . Finally, we show how one can recapture some of Al Alam’s results on boundedness and the essential norm of weighted composition operators...

On Halphen’s Theorem and some generalizations

Alcides Lins Neto (2006)

Annales de l’institut Fourier

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Let $M^{n}$ be a germ at $0 \in ℂ^{m}$ of an irreducible analytic set of dimension $n$ , where $n \geq 2$ and $0$ is a singular point of $M$ . We study the question: when does there exist a germ of holomorphic map $φ : (ℂ^{n}, 0) \to (M, 0)$ such that $φ^{- 1} (0) = {0}$ ? We prove essentialy three results. In Theorem 1 we consider the case where $M$ is a quasi-homogeneous complete intersection of $k$ polynomials $F = (F_{1}, ..., F_{k})$ , that is there exists a linear holomorphic vector field $X$ on $ℂ^{m}$ , with eigenvalues $λ_{1}, ..., λ_{m} \in ℚ_{+}$ such that $X (F^{T}) = U \cdot F^{T}$ , where $U$ is a $k \times k$ matrix with entries in $𝒪_{m}$ . We prove that if...

A characterization of linear automorphisms of the Euclidean ball

Hidetaka Hamada, Tatsuhiro Honda (1999)

Annales Polonici Mathematici

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Let B be the open unit ball for a norm on $ℂ^{n}$ . Let f:B → B be a holomorphic map with f(0) = 0. We consider a condition implying that f is linear on $ℂ^{n}$ . Moreover, in the case of the Euclidean ball , we show that f is a linear automorphism of under this condition.

Estimates for the Bergman and Szegö projections in two symmetric domains of $ℂ^{n}$

David Bekollé, Aline Bonami (1995)

Colloquium Mathematicae

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Small divisors and large multipliers

Boele Braaksma, Laurent Stolovitch (2007)

Annales de l’institut Fourier

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We study germs of singular holomorphic vector fields at the origin of $ℂ^{n}$ of which the linear part is $1$ -resonant and which have a polynomial normal form. The formal normalizing diffeomorphism is usually divergent at the origin but there exists holomorphic diffeomorphisms in some “sectorial domains” which transform these vector fields into their normal form. In this article, we study the interplay between the small divisors phenomenon and the Gevrey character of the sectorial normalizing...

Displaying similar documents to “Effective local finite generation of multiplier ideal sheaves”

On microlocal analyticity of solutions of first-order nonlinear PDE

Embedding theorems for Müntz spaces

On Halphen’s Theorem and some generalizations

A characterization of linear automorphisms of the Euclidean ball

Estimates for the Bergman and Szegö projections in two symmetric domains of ℂ n

Small divisors and large multipliers

Estimates for the Bergman and Szegö projections in two symmetric domains of $ℂ^{n}$