An essay on the Interpolation Theorem of Józef Marcinkiewicz - Polish patriot
In this paper we present an approximation to the de Rham theorem for simplicial sets with any coefficients based, using simplicial techniques, on Poincaré's lemma and q-extendability.
We give a proof of the fact that any holomorphic Pfaffian form in two variables has a convergent integral curve. The proof gives an effective method to construct the solution, and we extend it to get a Gevrey type solution for a Gevrey form.
Second order anti-holonomic jets as anti-symmetric parts of second order semi-holonomic jets are introduced. The anti-holonomic nature of the Lie bracket is shown. A general result on universality of the Lie bracket is proved.
An index theorem for the anti-self-dual deformation complex on anti-self-dual orbifolds with cyclic quotient singularities is proved. We present two applications of this theorem. The first is to compute the dimension of the deformation space of the Calderbank–Singer scalar-flat Kähler toric ALE spaces. A corollary of this is that, except for the Eguchi–Hanson metric, all of these spaces admit non-toric anti-self-dual deformations, thus yielding many new examples of anti-self-dual ALE spaces. For...
Nous appliquons les résultats d’un article précédent au domaine des fonctions différentiables. Nous obtenons en particulier des théorèmes de division et des théorèmes de fonctions composées.