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Displaying similar documents to “On the global solvability of linear partial differential equations with constant coefficients in the space of real analytic functions”

Constructible functions on 2-dimensional analytic manifolds.

Isabelle Bonnard, Federica Pieroni (2004)

Revista Matemática Complutense

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We present a characterization of sums of signs of global analytic functions on a real analytic manifold M of dimension two. Unlike the algebraic case, obstructions at infinity are not relevant: a function is a sum of signs on M if and only if this is true on each compact subset of M. This characterization gives a necessary and sufficient condition for an analytically constructible function, i.e. a linear combination with integer coefficients of Euler characteristic of fibers of proper...

On the intersection product of analytic cycles

Sławomir Rams (2000)

Annales Polonici Mathematici

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We prove that the generalized index of intersection of an analytic set with a closed submanifold (Thm. 4.3) and the intersection product of analytic cycles (Thm. 5.4), which are defined in [T₂], are intrinsic. We define the intersection product of analytic cycles on a reduced analytic space (Def. 5.8) and prove a relation of its degree and the exponent of proper separation (Thm. 6.3).

A microlocal version of Cartan-Grauert's theorem

I. V. Maresin, A. G. Sergeev (1998)

Annales Polonici Mathematici

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Tuboids are tube-like domains which have a totally real edge and look asymptotically near the edge as a local tube over a convex cone. For such domains we state an analogue of Cartan’s theorem on the holomorphic convexity of totally real domains in ℝ n ⊂ ℂ n .