A new characterization of the analytic surfaces in $\mathbb{C}^3$ that satisfy the local Phragmén-Lindelöf condition

Rüdiger W. Braun; Reinhold Meise; B. A. Taylor

Displaying similar documents to “A new characterization of the analytic surfaces in $ℂ^{3}$ that satisfy the local Phragmén-Lindelöf condition”

Perturbation results for the local Phragmén-Lindelöf condition and stable homogeneous polynomials.

Rüdiger W. Braun, Reinhold Meise, B. Alan Taylor (2003)

RACSAM

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The local Phragmén-Lindelöf condition for analytic varieties in complex n-space was introduced by Hörmander and plays an important role in various areas of analysis. Recently, new necessary geometric properties for a variety satisfying this condition were derived by the present authors. These results are now applied to investigate the homogeneous polynomials P with real coefficients that are stable in the following sense: Whenever f is a holomorphic function that is defined in some neighborhood...

Localizations of partial differential operators and surjectivity on real analytic functions

Michael Langenbruch (2000)

Studia Mathematica

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Let P(D) be a partial differential operator with constant coefficients which is surjective on the space A(Ω) of real analytic functions on an open set $Ω \subset ℝ^{n}$ . Then P(D) admits shifted (generalized) elementary solutions which are real analytic on an arbitrary relatively compact open set ω ⊂ ⊂ Ω. This implies that any localization $P_{m, Θ}$ of the principal part $P_{m}$ is hyperbolic w.r.t. any normal vector N of ∂Ω which is noncharacteristic for $P_{m, Θ}$ . Under additional assumptions $P_{m}$ must be locally hyperbolic. ...

Continuity of the relative extremal function on analytic varieties in ℂⁿ

Frank Wikström (2005)

Annales Polonici Mathematici

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Let V be an analytic variety in a domain Ω ⊂ ℂⁿ and let K ⊂ ⊂ V be a closed subset. By studying Jensen measures for certain classes of plurisubharmonic functions on V, we prove that the relative extremal function $ω_{K}$ is continuous on V if Ω is hyperconvex and K is regular.

A necessary condition of local solvability for pseudo-differential equations with double characteristics

Fernando Cardoso, François Trèves (1974)

Annales de l'institut Fourier

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Pseudodifferential operators $P (x, D) \sim \sum_{j = 0}^{+ \infty} P_{m - j} (x, D)$ are studied, from the viewpoint of local solvability and under the assumption that, micro-locally, the principal symbol factorizes as $P_{m} = Q L^{2}$ with $Q$ elliptic, homogeneous of degree $m - 2$ , and $L$ homogeneous of degree one, satisfying the following condition : there is a point $(x_{0}, ξ^{0})$ in the characteristic variety $L = 0$ and a complex number $z$ such that $d_{ξ} Re (z L) \neq 0$ at $(x_{0}, ξ^{0})$ and such that the restriction of $Im (z L)$ to the bicharacteristic strip of $Re (z L)$ vanishes of order $k < + \infty$ at $(x_{0}, ξ^{0})$ , changing sign there from...

A sufficient condition for existence of real analytic solutions of P.D.E. with constant coefficients, in open sets of $ℝ^{2}$

Giuseppe Zampieri (1980)

Rendiconti del Seminario Matematico della Università di Padova

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A new necessary condition for analytic varieties satisfying the local Phragmén-Lindelöf condition

Tobias Heinrich (2005)

Annales Polonici Mathematici

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For an analytic variety V in ℂⁿ containing the origin which satisfies the local Phragmén-Lindelöf condition $P L_{l o c} (0)$ it is shown that for each real simple curve γ and each d ≥ 1 the limit variety $T_{γ, d} V$ satisfies the strong Phragmén-Lindelöf condition (SPL).

On the dimension of secant varieties

Luca Chiantini, Ciro Ciliberto (2010)

Journal of the European Mathematical Society

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In this paper we generalize Zak’s theorems on tangencies and on linear normality as well as Zak’s definition and classification of Severi varieties. In particular we find sharp lower bounds for the dimension of higher secant varieties of a given variety $X$ under suitable regularity assumptions on $X$ , and we classify varieties for which the bound is attained.

Overstability and resonance

Augustin Fruchard, Reinhard Schäfke (2003)

Annales de l’institut Fourier

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We consider a singularity perturbed nonlinear differential equation $ε u^{'} = f (x) u + + ε P (x, u, ε)$ which we suppose real analytic for $x$ near some interval $[a, b]$ and small $| u |$ , $| ε |$ . We furthermore suppose that 0 is a turning point, namely that $x f (x)$ is positive if $x \neq 0$ . We prove that the existence of nicely behaved (as $ϵ \to 0$ ) local (at $x = 0$ ) or global, real analytic or $C^{\infty}$ solutions is equivalent to the existence of a formal series solution $\sum u_{n} (x) ε^{n}$ with $u_{n}$ analytic at $x = 0$ . The main tool of a proof is a new “principle of analytic continuation” for...

Estimates of the number of rational mappings from a fixed variety to varieties of general type

Tanya Bandman, Gerd Dethloff (1997)

Annales de l'institut Fourier

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First we find effective bounds for the number of dominant rational maps $f : X \to Y$ between two fixed smooth projective varieties with ample canonical bundles. The bounds are of the type ${A \cdot K_{X}^{n}}^{{B \cdot K_{X}^{n}}^{2}}$ , where $n = \dim X$ , $K_{X}$ is the canonical bundle of $X$ and $A, B$ are some constants, depending only on $n$ . Then we show that for any variety $X$ there exist numbers $c (X)$ and $C (X)$ with the following properties: For any threefold $Y$ of general type the number of dominant rational maps $f : X \to Y$ is bounded above by $c (X)$ . ...

The finiteness of compact varieties in $C^{n}$

Walter Rudin (1981)

Annales Polonici Mathematici

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Displaying similar documents to “A new characterization of the analytic surfaces in ℂ 3 that satisfy the local Phragmén-Lindelöf condition”

Displaying similar documents to “A new characterization of the analytic surfaces in $ℂ^{3}$ that satisfy the local Phragmén-Lindelöf condition”