Displaying similar documents to “Regular analytic transformations of ℝ 2 ”

Intersection theory and separation exponent in complex analytic geometry

Ewa Cygan (1998)

Annales Polonici Mathematici

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We consider the intersection multiplicity of analytic sets in the general situation. We prove that it is a regular separation exponent for complex analytic sets and so it estimates the Łojasiewicz exponent. We also give some geometric properties of proper projections of analytic sets.

Implicit function theorem for locally blow-analytic functions

Laurentiu Paunescu (2001)

Annales de l’institut Fourier

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In this paper we prove the implicit function theorem for , and as an interesting application of using blow-analytic homeomorphisms, we describe a very easy way to resolve singularities of analytic curves.

Failure of analytic hypoellipticity in a class of differential operators

Ovidiu Costin, Rodica D. Costin (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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For the hypoelliptic differential operators P = ∂ x 2 + x k ∂ y - x l ∂ t 2 introduced by T. Hoshiro, generalizing a class of M. Christ, in the cases of k and l left open in the analysis, the operators P also fail to be analytic hypoelliptic (except for ( k , l ) = ( 0 , 1 ) ), in accordance with Treves’ conjecture. The proof is constructive, suitable for generalization, and relies on evaluating a family of eigenvalues of a non-self-adjoint operator.