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Analytic extension from non-pseudoconvex boundaries and A ( D ) -convexity

Christine Laurent-Thiébaut, Egmon Porten (2003)

Annales de l’institut Fourier

Let D n , n 2 , be a domain with C 2 -boundary and K D be a compact set such that D K is connected. We study univalent analytic extension of CR-functions from D K to parts of D . Call K CR-convex if its A ( D ) -convex hull, A ( D ) - hull ( K ) , satisfies K = D A ( D ) - hull ( K ) ( A ( D ) denoting the space of functions, which are holomorphic on D and continuous up to D ). The main theorem of the paper gives analytic extension to D A ( D ) - hull ( K ) , if K is CR- convex.

Global time estimates for solutions to equations of dissipative type

Michael Ruzhansky, James Smith (2005)

Journées Équations aux dérivées partielles

Global time estimates of L p - L q norms of solutions to general strictly hyperbolic partial differential equations are considered. The case of special interest in this paper are equations exhibiting the dissipative behaviour. Results are applied to discuss time decay estimates for Fokker-Planck equations and for wave type equations with negative mass.

Hartog's phenomenon for polyregular functions and projective dimension of related modules over a polynomial ring

William W. Adams, Philippe Loustaunau, Victor P. Palamodov, Daniele C. Struppa (1997)

Annales de l'institut Fourier

In this paper we prove that the projective dimension of n = R 4 / A n is 2 n - 1 , where R is the ring of polynomials in 4 n variables with complex coefficients, and A n is the module generated by the columns of a 4 × 4 n matrix which arises as the Fourier transform of the matrix of differential operators associated with the regularity condition for a function of n quaternionic variables. As a corollary we show that the sheaf of regular functions has flabby dimension 2 n - 1 , and we prove a cohomology vanishing theorem for open...

Hypercyclicity of convolution operators on spaces of entire functions

F.J. Bertoloto, G. Botelho, V.V. Fávaro, A.M. Jatobá (2013)

Annales de l’institut Fourier

In this paper we use Nachbin’s holomorphy types to generalize some recent results concerning hypercyclic convolution operators on Fréchet spaces of entire functions of bounded type of infinitely many complex variables

On D*-extension property of the Hartogs domains.

Do Duc Thai, Pascal J. Thomas (2001)

Publicacions Matemàtiques

A complex analytic space is said to have the D*-extension property if and only if any holomorphic map from the punctured disk to the given space extends to a holomorphic map from the whole disk to the same space. A Hartogs domain H over the base X (a complex space) is a subset of X x C where all the fibers over X are disks centered at the origin, possibly of infinite radius. Denote by φ the function giving the logarithm of the reciprocal of the radius of the fibers, so that, when X is pseudoconvex,...

On envelopes of holomorphy of domains covered by Levi-flat hats and the reflection principle

Joël Merker (2002)

Annales de l’institut Fourier

In the present paper, we associate the techniques of the Lewy-Pinchuk reflection principle with the Behnke-Sommer continuity principle. Extending a so-called reflection function to a parameterized congruence of Segre varieties, we are led to studying the envelope of holomorphy of a certain domain covered by a smooth Levi-flat “hat”. In our main theorem, we show that every 𝒞 -smooth CR diffeomorphism h : M M ' between two globally minimal real analytic hypersurfaces in n ( n 2 ) is real analytic at every point...

On the removable singularities for meromorphic mappings.

Evgeny M. Chirka (1996)

Publicacions Matemàtiques

If E is a closed subset of locally finite Hausdorff (2n-2)-measure on an n-dimensional complex manifold Ω and all the points of E are nonremovable for a meromorphic mapping of Ω E into a compact Kähler manifold, then E is a pure (n-1)-dimensional complex analytic subset of Ω.

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